I figured I'd make a thread about this since I haven't seen it discussed before and it's an easy way to level enchanting.

A quick way to level enchanting is to recharge weapon enchantments with soul gems. An easy way to do this is to use the Azura's star and a weapon with the Soul Trap enchantment. This works because the Azura's Star is a soul gem that doesn't break upon use.

1: Grab the Azura's star from this quest: uesp.net/wiki/Skyrim:The_Black_Star
2. Enchant a weapon with soul trap.
3. Your only empty soul gem should be the star, this will make things go faster.
4. Get a kill with your soul trap weapon, it will fill the star.
5. Use the star to refill the weapon (even though it's only one use you get the same xp as a full restore).
6. Repeat steps 4-5, this will raise enchanting.

If you have any questions, ask them here or pm me, I'm happy to help.