(aka "WTF How the Bloody Hell is This Stuff Supposed to Work Anyway?!")
Since the BBC tv series Merlin is about...well...Merlin, magic is naturally an important part of the universe. But unfortunately, we don't have a handy magic book or our own that explains the rules of magic - how it works, what's involved in the process, and what exactly it can do. This is complicated by inconsistencies in the series itself, and the fact that we have a character who is categorically stated to be "different". In fact, the most realistic explanation for all of the magic we see in the series is "the writers hate continuity." But, particularly for the sake of things like fanfiction and roleplaying, if we want to have anything resembling a coherent theory of magic we have to watch the show closely and try to come up with it ourselves.
And, since I evidently am insane and have way too much time on my hands, I will attempt to try. To make this analysis, I will be relying on two sources - archaeologist_d's List of Spell Translations and my List of Magic Performed. I will also, of course, be using the show itself and what the narrative tells us about magic.
This post contains spoilers for Merlin Seasons 1-3, so please be warned!
All we see of the process of casting magic is people sometimes making gestures, sometimes using incantations, and sometimes not doing anything except looking in the general direction of whatever it is they want to do magic on. In fact, we never actually see any kind of action that consistently accompanies the use of magic, other than perhaps the looking. But there needs to be more to it, because just looking at stuff was all that was required, all the sorcerers would have to be like Cyclops and wear strange protective eyegear to stop them magicing everything they look at.
So what do we know? Well, as I will detail later, incantations aren't necessary, so it's not a case of just knowing the right words. We know that it normally takes years to study, as stated by Gaius and backed up by the fact that even after a year spent with Morgause, Morgana's magic is still mostly limited to uncontrolled bursts of magic, or the occasional simple spell. Anything more complicated, and she needs involves an additional aid (like the rowan staff) and guidance from Morgause. We know that it takes concentration and focus of will, also thanks to Gaius. And it's this that, to me, seems to be at the heart of how exactly magic is performed. Rather than being a case of "knowing the right words of actions", the casting of magic is more like kind of metal exercise. Other forces may assist or enhance the magic - like incantations, the Sidhe staffs, or various other magical objects - but in essence what's required is the sorcerer's focus of will.
But if magic is just a mental exercise, it does bring up another important question: why on earth do they need spellbooks? If it were just a case of, "if I will it hard enough it will happen", Merlin wouldn't need to run around looking up stuff.
So what do spellbooks do? Well, I'd like to theorise that what they are is a kind of guide, with suggested incantations and instructions on exactly how the sorcerer should focus their will. If magic is a mental exercise, then it makes sense that there are also little mental tricks that go along with it - like perhaps focusing on a mental images, or remembering a feeling. Simple spells might require just one element - like perhaps imagining just one mental image - while more complex spells might require multiple elements, or a complicated mental trick. This then, would be the purpose of the spellbooks - to detail the best mental tricks and guide the sorcerer through them.
This also serves as an explanation for why magic takes years to study - because effectively, sorcerers have to learn how to use all the metal tricks, and how to focus their mind in a way that lets them perform these mental gymnastics.
At first glance, it would appear as if incantations are the main driving force behind magic - speak the magic words, yadda yadda yadda, stuff happens. And from watching the show, you might get the impression that each spell has a set incantation - that Merlin looks up the Magic Words in his book, and that's the One True Way to cast whichever spell he wants to do. But as I've already suggested, and as a look at the translations of the spells shows, this isn't the case. Because we have translations like this:
Go, boots. Stall, boots. Guide the boots.
This is the spell that Merlin uses to move the boots in Morgana's chamber, in S1E8 - and it's bizarre specific to the situation. This is not a spell that you would sit down an learn (and if you've been spending your time learning random spells to move boots, then I'm afraid you're beyond all help Merlin). And this isn't the only example - a close look at archaeologist_d's translations shows there are many other spells which are similarly situation-specific.
Not only that; we also get Merlin using different incantations to essentially do the same thing. In S2E6, Merlin locks a cabinet with the incantation "Fyrbendum faest", meaning "the secure forged bars". And then in S2E10, he locks a cupboard with the incantation "Behaepse faest", meaning "fasten a closed door". He's essentially doing the exact same thing but with a different incantation.
And this isn't the only peculiarity regarding incantations - right in the first episode, when we have Merlin using magic without any incantations at all, Gaius says that incantations are required for magic. This is also when Gaius states that Merlin that he is "special", that no one else does magic like him. The implication is that everyone else needs incantations, but Merlin doesn't because he's just awesome like that. Except, Merlin doesn't actually seem that unique in this regard. We see a whole range of characters other than Merlin using magic without incantations - Anhora, Cornelius Sigan, Edwin Muirden, Mordred, Morgana, Morgause, Nimueh, and Trickler. Even in the first episode, we get Mary Collins using magically killing a girl just by touching her and humming. If it were only characters like Sigan, Mordred, Morgana, Morgause and Nimueh not using incantations, we could pass it off as being an "Old Religion" thing, but that doesn't explain characters like Edwin and Trickler doing it. At this rate, everyone and their mother is doing incantationless magic.
One possible explanation is that Gaius was just plain wrong. He is, after all, implied to have only ever been a mediocre sorcerer. But I'm inclined to disagree with the idea that Gaius just doesn't know what he's talking about - because while Gaius might not be good at magic, he is shown to nonetheless be very knowledgeable about it. And with so many characters running around not using incantations, I can't see how he would have missed them all.
So why is Gaius so surprised by Merlin's lack of incantations in the first episode? And why do all of these characters who don't even need incantations keep using them when they risk being heard and discovered? Do all sorcerers just have an inexplicable urge for dramatics? Do they just really like the sounds of the own voices?
Gaius himself gives one possibility: he asks Merlin if he's reciting the incantations in his mind. This would suggest that everyone other than Merlin is in fact saying incantations in their heads. But, my personal theory is that there is more to this: incantations aren't actually necessary at all. What they are is simply a focus for the sorcerer: a way of concentrating their mind on what they want to do. This is why you get situation specific incantations and different incantations for the same thing: the actual words are irrelevant. What really matters is having something to focus your magic on, so that it does what you want it to and not something else. A guide, perhaps, for those mental gymnastics that all these sorcerers are doing. This would explain why when Morgana's magic started flaring up it was out of her control - she hadn't learned how to do the mental gymnastics and she didn't know how to use incantations to help focus her magic, and so it got away from her control.
A FLASH OF GOLD
This is one of the areas of magic that suffers the most from inconsistency - whether or not the caster's eyes flash gold when they use magic. In the first season, this seems to be a trait unique to Merlin. But then in season two we see other characters also having the gold eyes. Namely, Morgana and Morgause. But, this doesn't necessarily contradict the idea of the gold eyes being something special and unusual. After all, Morgan le Fay in the legends is frequently a sorceress on par with Merlin, and Morgause has connections to the Old Religion. Gold eyes, then, could just be an Old Religion thing.
But then in the third season we anyone with magic showing gold eyes - hell, even Gaius gets them - which pretty much reduces and any all specialness about them.
So what do they indicate? Well, the most likely explanation is that the show's makers have forgotten their own rules and just use them whenever they feel like it. Particularly since the inconsistency is so bad that it's pretty much impossible to come up with a unified theory that doesn't contradict half of the show. But, we will nonetheless examine the possibilities, and how plausible an explanation they might be.
Firstly: only Merlin has the gold eyes. He's just Special and so he's the only one who gets to have them. The major downside to this theory is that it requires pretending that Morgana, Morgause, and everyone else having them later on is wrong and never happened. Out of all the possibilities, this one is the least likely.
Secondly: only people who are of the Old Religion have the gold eyes. This explains Merlin, Morgana, and Morgause, but not why even Gaius gets them later on. It also doesn't explain why Nimueh doesn't have them. This is the least likely theory after the "it's just Merlin" one, since it requires pretending that both later examples were wrong and that earlier examples of where gold eyes should have shown up but didn't are also wrong.
Thirdly: everyone has magic had gold eyes when they do it. Ever. No exceptions. And in seasons one and two, they were just really lazy and didn't have the budget to give them to everyone. This theory is considerably more logical than the first two, although a bit of pretending is still involve.
And one last theory: the gold eyes are merely symbolic. Magic user's eyes don't actually change colour at all - it's just a visual metaphor the writers are using to indicate the use of magic. Thus, it's actually a tool of emphasis for the writers: in the first season Merlin is what they want to emphasize, so we only see it with him. Then when Morgana and Morgause start flinging magic around, the writers wanted to emphasize that. And then in season three they just decided to emphasize all magic ever. This would also explain why we never see any character's remarking on people's eyes changing colour within the context of the show. In fact, of all the theories this one is the most logical of all, and the only one that explains the use of the gold eyes through the run of the entire show.
Course, that theory is also much less fun and denies fanfic writers everywhere to the opportunity to have Arthur go on about Merlin's eyes turning gold. But for the sake of fanfic everywhere, I think the explanation of all magic users having the gold eyes is the most tenable explanation. Still, since at the root of this lies an undeniable inconsistency - I mean, we see Gaius using magic with both normal eyes and gold eyes - this really is a case of "pick your own theory and go with it" when it comes to fanfic and the like.
As an afterthought: while no one ever remarks on anyone's eyes turning gold, what we do see is Gaius directly mentioning the Sidhe's eyes, and their colour. If the "everyone with magic gets gold eyes" theory is correct, then it makes sense that the Sidhe's eyes are a different colour because they have a different kind of magic.
MAGIC AND INHERITANCE
We know that Merlin himself was born with magic: but what about everyone else? Is magic an inherited trait, or is it a case of "you only know it if you learn it"? Certainly, characters like Uther give the impression that they beleive that magic is a choice, not something inherent. Uther frequently rationalises that people with magic have chosen it, and thus in his mind have also chosen 'evil'. This view implies that magic isn't inherited - after all, if you can't choose what you are born with.
But the show categorically states that there are, at the very least, some kinds of magic that are inherent. First, we have seers like Morgana. Gaius states that the seer's ability is innate: you either have it or you don't. But, we don't know whether this ability is passed on genetically: there's no indication that Morgause is a seer, and with Uther and Arthur being the only other relations of Morgana that we know of, we don't have any way of comparing Morgana with others on her family tree.
Secondly, we have the dragonlords, whose abilities are stated to pass down from "father to son". This is a clear case of magic being passed on genetically - although the fact that they apparently can only be inherited on the death of the father is, quite frankly, rather bizarre. It's also problematic - what if a dragonlord had multiple sons? Would only one of them get the abilities on his death? And how many dragonlords were offed by their own sons because said sons didn't want to wait to get the power? And what about girls - were there really no dragonladies, or were dragonlords were just sexist? Maybe they didn't consider girls really 'capable' of commanding dragons, even if they had the power. The fact that Merlin doesn't command the dragon at all until Balinor kicks the bucket does seem to suggest that Balinor needed to die before he could get the power, but this is complicated by the fact that Merlin didn't know that he might be able command the dragon. As far as he knew it wasn't even possible, so he never even tried. Personally, I like to think that Gaius just claimed that Merlin couldn't inherit dragonlord powers until Balinor was dead because Merlin was quite clearly doubting his ability to do so. Course, "it's just works that way by magic" is a just as valid explanation for the bizarre genetics of this.
But, getting back to the other magic users - your average sorcerer or sorceress who just has "magic" and not any other fancy abilities - are their powers inherited as well? Were they born with them, or did they only gain magic once they started to learn it? The fact that magic often seems to run in families does suggest a genetic link - for instance, we have Mary Collins and her son, the sisters Morgana and Morgause, and Gilli and his father. We also see cases of magic being used without any kind of teaching at all - Merlin being the obvious example. And, we also have Morgana - she might not be using it from birth, but she quite clearly begins to use magic without any kind of formal teaching whatsoever. This doesn't give us much to go on, since other than these two we don't ever see any other untrained magic users. But, I would theorise that some of the drowned children and other people executed for magic before Merlin's arrival were like Morgana, and just people who inherently had magic and used it accidentally.
However, there is another discrepancy which we need to address. On the one hand we have Merlin who is using magic as a baby, and on the other hand we have Morgana who shows no sign (apart from her visions) until adulthood. But is it really valid to just say, "Merlin is a freak" and leave it at that? Merlin's quite clearly unusual, but do we really have him in his own special little box and everyone else in another?
I'd like to argue that there in fact exists a continuum of magic: at one end, we'd have people who have no magic whatsoever and who could never learn it, even if they tried. We'll call this the "Arthur" end of the spectrum, since this is how many fanfics portray him. (Although we can't say for certain if Arthur actually is this, since he's never even tried to learn magic. Actually, Arthur trying to learn magic would probably make an interesting fanfic--but, I'll get back to the point.) I would imagine that a significant amount of the population sits here in this magicless part of the continuum. And on the other end, we have people like Merlin who use magic instinctively from infancy. The "Merlin" end of the spectrum is clearly the extreme - after all, it consists of...well, just Merlin. But everyone else would sit somewhere in the middle of these two sides, with some being closer to the "Arthur" end and others closer to the "Merlin" end.
Morgana, for example, is clearly closer to the "Merlin" end; but not close enough to manifest accidental magic in infancy. Mordred is possibly even closer to the "Merlin" end than Morgana, although it's hard to know for sure since he's already been taught magic. In the other direction, closer to the "Arthur" end, we have characters like Gilli, and Gaius. Gilli has magic, but needs an enchanted ring in order to support his powers, while Gaius's magic is woeful unless he actively practises it and works at it. Chances are, neither Gilli or Gaius ever exhibited any kind of accidental magic - they probably had to be taught. And I'd argue that most people who have magic actually sit in this same middle-to-lower area - they have the potential to use magic, and can perform it adequately if they learn, but they don't have enough innate ability to start accidentally using it. In fact, there's probably a significant group of people who have magic and don't know it, just because they've never tried.
HOW SPECIAL IS A SPECIAL SNOWFLAKE?
On a final note: it's pretty clear from the narrative that Merlin is meant to be something different. He's supposed to be unique, and not quite like other sorcerers. He has Gaius telling him that 'no one' is like him, he's got a mountain of prophecies about him, a dragon giving him cryptic remarks about his great 'destiny'...not to mention the fact that we all know that he'll eventually be known as the greatest wizard of all time.
However, the show doesn't actually do that much to show us how Merlin is different.
While in the first season only Merlin's eyes flash gold, by the time we get to season three everyone and their mother is flashing them around. Gaius makes a big fuss about how Merlin performs magic without incantations and how that 'isn't possible', but again we have a long list of people other than Merlin who use wordless magic. And he's also not the only one we see performing magic without teaching - Morgana also shows signs of magic without any lessons at all. Sure, he is the only dragonlord - but that's only because all the other dragonlords are conveniently dead. Merlin, it seems, is a special snowflake that's not actually that special. He's clearly on the extreme end of the spectrum, yes - but this doesn't actually make him a one of a kind, freakish thing that no one's ever seen the like of. It just makes him someone who happens to sit higher on the bell curve than everyone else.
Still, if we get out a magnifying glass and look really closely, we can find something that is still unique about Merlin - the fact that he can use magic instinctively. Merlin doesn't actually need "the process" of mental gymnastics that other sorcerers need - sure, he can still use it and for many spells he finds focusing his will useful - but for him it's not necessary. This is what what surprises Gaius about the fact that Merlin's not using incantations in the first episode - it's that he's doing magic without any focus at all. For him it "just happens". And even Morgana, who's closest to Merlin in terms of "using magic without learning", doesn't use magic instinctively. Sure, she has incidents of magic - but it's a wild, out of control thing. She's not using magic, it just happens to be leaping out of her. Whereas Merlin can use magic instinctively, and control it, without ever having any teach him how to focus his will.
Course, in the end once Merlin starts learning magic properly the end result is the same. So he's still a little special, and still freakishly high on the spectrum of magical power.