I have all the spells, and I know they work, because illuminate works and the teleroll works when I roll. I am using a keyboard, and I cannot figure out how to cast spells. pressing "M" does not do anything. I am trying to cast fireball.
After equipping, many spells, including fireball, must be selected on your ability quickslot which is toggled with '3.' Then, hold 'M' or 'middle-mouse' until cast. There's a stamina requirement so you may need to level up and increase your Endurance for some spells, though.
Also, we're not sure, but the summoning spells may be broken...