Skyrim Walkthrough: Ep. 13 Fast Leveling Destruction (auluftwaffles.wordpress.com)

In Oblivion you could conjure a being and then kill it with destruction magic. This is also the case for Skyrim. The destruction is slow to level up, but using the technique outlined below you can concentrate on leveling it up much more so than if you were just doing some quests.

What you want to do is cast a being using the conjugation school of magic. Because I am not focusing on conjugation I only had the spell "conjure familiar" which I used. Then you can select any destruction spell and kill the creature you cast. If you have leveled up conjugation or have spells of creatures that have more health your destruction will level faster because it levels with the damage you do to a valid creature.

The master trainer for destruction magic is Farelda in the College of Winterhold. She can be found in the first hall when you enter the college through the gate to the right. Just peak in every alcove around the hall and she should be in one of them. However, as you can see in the video below, she was not there for me which I believe is due to the fact that I am in the middle of a quest for the Collage of Winterhold.