You can have one active spell at a time, which traditionally is your main low-cost attack spell, FireBall/IceLance/Lightning. I recomend you get one of them to begin with, and later you might want to get another since there are monsters resistant to specific damage types, but your demon can regulary take care of thoose (see later down)
To use your attack spell you simply target a monster and click. If you hold down your mousebutton for awhile instead of just tapping it, your spell will load up and do more damage and alo become homing.
You also want one of the areaattacks, Fire Rain for example. If you manage to position yourself somewhere where you cannot be reached, throwing several areaspells at the same place will very quickly annihilate a whole horde of enemies. There's a few places that becomes very useful.
The best defense you can get is a Demon. Summon Demon that is. Call him before a major battle and he will take the pain for you.
There are no personal defense spells, but I cannot see a mage go without healing. Healing is too slow to be used properly in combat though.
Beyond that you might want Light to lit up dark areas without occupying your hand with a torch. Heal Other is good to keep NPC friends alive.
The rest is up to you. Remember that you can only use one spell at a time, which unfortunally reduces the amount of spells you might want to use.