For the simplified version, refer to the Abilities and Weapons section on
Roy's profile.
Alchemy is a school of magic devoted to the transformation and manipulation of matter through ritual and symbols… it is one of the first and oldest schools, primitive compared to the sort of stuff one sees today, but brutally effective in its methods precisely because of its age. At first glance, it would seem as though alchemy is capable of creating something out of nothing - this could not be more false. The art is governed by the principle of equivalent trade: that is, one cannot transform an object into something that it is not made from the same components. Water, therefore, cannot be turned into fire, and vice versa. Also, in order to build a house, one must gather all of the needed components and but in all the needed effort - it cannot simply assemble itself of its own accord.
At the end of it all, what you give is what you get - if one wants something, one needs to sacrifice something of equivalent cost in order to receive it. The principle of equivalent trade is something that is both the main rule that binds the art of alchemy and a philosophy that all alchemists inherently subscribe to, as a matter of circumstance. It sounds simple enough, but that’s only if you’re dealing with inanimate objects, things that weren’t alive to begin with. There’s a reason why alchemists are forbidden from attempting to create life - while one can come up with all the material components, mimicking the sentience is quite another thing altogether.
That’s not to say that people haven’t tried, with terrible consequences.
The creation of life aside, it is impossible to do alchemy without transmutation circles, which are the result of years upon years of studying the runes and equations that allow the transmutation process to occur in the first place. The more complex the procedure, the more complex the circle, and the longer an alchemist will have to concentrate. The longer the concentration period, the more likely the alchemist in question will fail. Overall, it is incredibly difficult to do alchemy in battle, unless you’re keeping things simple.
On that note, let’s look at the three ways of doing alchemy. First, there is the deconstruction of matter into its component parts - this is the simplest procedure, as all it requires is an unraveling of what is already there. The second is a manipulation of present components - this one is slightly more complex, as the rules of equivalent trade demand that everything comes out even in the long run. The third is the actual transmutation, which involves both deconstruction and manipulation in order to turn one object into another. The type of alchemy that Roy does the most is manipulation, which he uses to create flames at the tip of his fingertips. It sounds like magic, but, true to his breeding as an alchemist, there’s a lot more science behind it than one thinks.
Roy carries a pair of white gloves on his person at all times - they don’t look like anything special to an outsider beyond the fact that they have transmutations inscribed upon their backs. In actuality, though, these gloves are actually lined on the outside with ferrocerium, a man-made alloy that, when scraped by any hard, sharp edge, is capable of producing sparks that are much hotter than that which can be obtained with your usual flint and steel. Roy created this gloves using alchemy, manipulating the ferrocerium in as much as he could and binding it to leather in order to create something that he can wear on his person and use with his flames without risking too much damage to himself.
In terms of actual alchemy, what Roy does is split air into its component parts (deconstruction), adjust the density of the oxygen around him according to his needs (manipulation) and set the more combustible components of the air (hydrogen being the foremost) on fire by generating friction with the ferrocerium on his gloves, whose sparks the hydrogen and other combustible components react to. As oxygen feeds fires, the amount of oxygen that Roy has to work with determines how far he can send his fire out, and allow for a remarkable amount of control given the fact that he’s literally playing with fire.
On another note, people commonly think that the snapping sound is a result of Roy snapping his fingers - it’s a signature of his down with his Academy buddies. In actuality, it’s the popping sound of the hydrogen and oxygen reacting together in the air.