How does magica work ?

[Cilia]

OK, let's do this.

On Magic
-Magic, probably, is the end result of aetheric manipulation. To cast a spell you need to gather, concentrate, and direct the aether to achieve the desired effect. To cast a fire spell, for instance, you just gather and direct a certain amount of fire aether from the environment / atmosphere. Aether is in all things, y'know...

Each class' method of doing so differs slightly, but that's the basics of it. To wit:
CNJ / WHM: Very druid-lite in this game, uses ambient aether for healing effects. Relies primarily on wind, water, and earth, based on their spells.
THM / BLM: Uses ambient and personal aether to produce various effects, relying primarily on fire (Astral) for high power and ice (Umbral) to slow down enemies and regain mana.
ACN / SCH / SMN: ACN uses aether to program Carbuncle familiars, with Emerald leaning towards wind and Topaz leaning towards earth. SCH uses the same type of aether as CNJ / WHM, probably, and uses a more advanced version of the Carbuncle familiars (the fairy summon has sentience, unlike a Carbuncle). SMN uses their personal aether to give shape to a pseudo-Primal from their memory; arguably, primal egis use as much of the SMN's aspected aether as is physically possible without adverse effects.
AST: Pulls in aether from the heavens. Somehow. I think.
PLD: If you think they're actively using magic, uses Light aether for mostly defensive purposes.
NIN: Uses small amounts of personal aspected aether to produce a variety of ninjutsu. Can only use ninjutsu at a limited rate to avoid problems with imbalanced internal aether.
DRK: Uses personal Dark aether to enhance attacks. Much more intense than ninjutsu, but capable of vampirically draining aether from enemies through various means.

In all cases, running down to 0 MP is probably the greatest amount of exertion that can be done without ill side effects. Fortunately, the only classes that dip down that low regularly are BLM and DRK, the former of whom does so intentionally before recovering with Umbral Ice and the latter of whom knows the risk of using too much of the power of darkness, so they cut it off before mental pollution and physical breakdown begin.

On Garleans
-Pretty sure they're not aliens. I believe it was stated somewhere that their inability to manipulate aether is because of a genetic defect, but I don't remember where from.