This is a very involved question, but I'll try and sum up.
* Magic works on a mana system. Mana points don't get that high; most common spells use 1-3 points of mana, while uber-spells would need things called Mana Stones (essentially mana batteries, some rechargeable, some not) plus other people contributing their own mana via Group Magic and so on.
* You learn individual spells much like you would learn skills and feats; 1 skill per spell, but some spells have prerequisites of other spells (example: Fireball would require Create Fire first, or you couldn't learn it).
* You must make a caster check to "activate" a spell. Once activated, you might have to make a combat check to lob, shoot, or maintain it. You can have any number of spells "on" at any time, but each additional spell makes casting other spells harder.
* Combat rounds in GURPS are ine 1-second increments. Casting damaging spells becomes a huge pain in this system; casting a Fireball (for example) nets you 1d6 the first second but you must "charge" the spell each second to get more damage potential. The trade-off is that a 3d6 Fireball will probably kill anyone in one hit... but most of your melee pals will have chopped your foes into bts by then. It's wonky like that.
* In the "default" Fantasy setting, no one may learn magic without the "Magery" advantage (like a feat). This advantage increases your effective skill levels for ALL your spells, though. Because of its character point (CP) expense, combined with the expense of learning spells in the first place, you will find very few 'dabblers' in the arcane arts.
* There are two GURPS gaming books chock full of magic spells (the Basic GURPS book having a few, well, basic spells), ALL of which are extremely nifty. GURPS Magic and GURPS Grimoire are a MUST (!!!) have for the wizards.
It's been a while since I've played GURPS. My first character ever was a jack-of-all-trades type who was very AD&D 2e Bard-like in capability. He was a Song Wizard; he had to be able to sing to cast spells, couldn't cast spells UNLESS he was singing, and enjoyed a cheaper spell cost to learn new magic as a trade-off.
Making GURPS characters in general is extremely (!) daunting at first. Limit yourself to the Basic rules until you become more familiar with the system. Then, start introducing spells from the other Magic books.
I've also found that the more GURPS books you buy, the more precarious it is to make characters as the wealth of options becomes overwhelming and you're never quite sure what's b0rken until you actually see it in play, which is usually much too late.
