Lesson 1: Dual-casting is For WIZARDS
Being a wizard, you'll never produce the DPS that a warrior can generate, but the one thing you do have going in your favor is dual casting. One spell. Both hands. And that dual-cast perk on the Destruction skill tree. You'll need that.
Just dual-cast a cheap, single-shot spell, like Firebolt, and you're almost guaranteed to stun your enemy, which is just about the best defensive measure a wizard can have, but remember to wait until your opponent is completely finished being stunned before dual-casting another spell, or it won't reset the stun.
Lesson 2: Never Pull Out Your Biggest Gun
|This troll is just asking for a firestorm to char him faster than dragon's breath, but control your urges, Wizard, and reserve your power!|
Whatever your biggest, most destructive spell is, you should never use it. Always use the second-strongest spell in your arsenal and dole out your magicka responsibly.
Of course, while this is logical advice, I've never been too good about following it, myself.
Lesson 2.5: Never Pull Out Your Biggest Gun, Unless it's Awesome
Lesson 3: Stun and Cook
|This pic doesn't have anything to do with casting a wall spell on a stunned enemy, but I just thought it looked cool.|
The wall spells are super cheap to cast, and if you can get your opponent to stand on top of one they'll suffer an incredible amount of damage. A well-timed, dual-cast Firebolt works perfectly to keep the badguy on top of your damage trap. The Paralyze spell from Alteration is even better.