Skyrim - How can I train myself as a mage?

I found destruction took me longer to train than any other school of magic.

As said above, the only real way to train Destruction is by using it on proper targets... enemy combatants. But there are a few tricks that can help you out.

First off, when you are training (especially just killing low level trash mobs like bandits) I make sure to NOT use dual-casting. When you land a spell, you get the same xp whether you use a powerfully charged spell or a weak one. So if you can force yourself to land 4 or 5 magic attacks on an enemy rather than 2 or 3, you will level up faster.

Second: Nerf yourself. This uses the same concept as the above advice. See an undead? Use frost spells. Undead are highly resistant to frost, and so you will need to use more spells to bring the target down. This will result in more xp per kill. Another example is using fire spells against Dark Elves or ANY magic against Bretons. You get the idea...

Thrid: Use respawns. The Aldmeri embassy in Solitude is a great place, as you can attack them all you want (if you are not seen by town guards) without gaining any bounty. So clear that place out every-time you are there. This always works with dungeons... most will respawn all their lower level creatures once a week. Those 4 dungeons/caves that are close to Riverun are another great farming location.

Fourth: You can always cheat. If you go far enough into the Dark Brotherhood quest line you get to ride our old friend Shadowmere. This is the fastest mount in the game, with near infinite hit points. Beat that horse.... literally.

Um... ok bye.

Well, it's all up to you. Easier, more rewarding, or more powerful is all a matter of opinion in this game. Any type can be great with the perks system in the game, it's just about your individual playstyle. For my personal playstyle, I get the most out of being a warrior. Don't get me wrong, my mage is a blast (literally), but with my personality I just prefer going toe-to-toe with baddies and confronting my enemies head on with a sword. One of my friends is the exact opposite. She'd rather blast away from a safe distance and use summoned creatures instead. Each style is effective if you build it right, just different. Just play each for a bit longer and you'll figure out what works for you.

Join the College of Winterhold, you can buy a ride there from the carriage in front of Whiterun, in the stables. That's a good place to start. And to level your skill just go to every dungeon and kill everything using destruction. It only levels if the things you're fighting are decent matches for you. So no killing bunnies to get levels. (Thats just cruel anyway xD)

go to the college in winterhold, and got some equipment (ropes and stuff) train in most in magica a bit in health and in stamina eavery now and then. try get the dremora lord.

and just keep using spells (but carry a sword or dagger in emergencies)

and good luck :D