By default, you can put two skills on your mouse buttons, and another five on the 1-5 keys. The fist two you click on an enemy to cast, or hold shift to hard-cast it. 1-5 you just press the button and it casts the spell at your mouse target.
You can also re-bind the extra slots to also be buttons on your mouse, though I haven't had to fiddle with that since my mouse already has a numpad on it that works for the number keys just fine.