Well you have to either buy books/spells or get them from monster drops (which are quite frequent). They have to match your class of course. There are some basic skills each race is allowed to get, but everything else is class specific.
So once you pass level 10 and choose your class, say your a Templar for example. You would go to the class trainer, and buy the first few levels of whatever spell/ability you wanted to use, granted you have the minimum stamina or whatever requirement it is. Then once in your inventory, you right click the book or spell and it goes into your skill list, which you can get to by hitting K. You then put the spell or ability in your quick slot on the bottom of the screen, you can just left click the spell once, then left click again in one of the quick slot slots. Then you press the corresponding key, say 1 for some uber magical attack thingie. This will put the skill/spell into the currently selected box next to the quick slots. Then when you are in battle, right click your mouse and enjoy the fireworks.
That's a simple run down of course. You can put food and other things in the quick slots, some of which you don't need to activate (food for example) where you can just press the key, 8 for example, to activate it.