This is kind of an exploit, but what I did to level up Enchanting fast was...
1) First make sure you have a decent amount of gold, 10,000g or more. A good way to make gold fast is to pickpocket rings and necklaces off various npcs and sell them. Just 7 points into pickpocket can net you tons of gold. You can easily level it by training pickpocketing from Silda in Windhelm, SAVE GAME then pickpocket until you get the gold back without getting caught. If your low level, this will level you fast, so be prepared for that. You can also use the rings and necklaces to enchant.
2) Go to Adrianne in Whiterun, buy all the Iron Ore and Ingots off her. SAVE GAME. Kill her. LOAD GAME. She should have restocked all her iron (and gold; this works with all merchants and is useful for selling that jewelry you stole, ;P). Repeat until you have lots of iron. Also buy some Leather and Leather Strips.
3) Smelt the ore you have. Turn all your leather unto strips. You should have an equal amount of Iron Ingots and Leather Strips. Use the materials to make Iron Daggers. This method will quickly level your Smithing and as well as your character, so be prepared for that. Also, each time you level, it will also be a good idea to pay a visit to a trainer with a skill you don't plan on using much (5 free skill ups with pickpocket).
4) Go to Dragonsreach Hold. Farengar occasionally sells Petty Soul Gems filled with souls already. Buy these, SAVE GAME, kill him, LOAD GAME, repeat. Repeat until you have a good amount of gems.
5) Head to the enchanting table near by. Make sure you have any kind of weapon enchant, if you do not, buy a weapon with an enchant from a vendor and disenchant it to learn it. Enchant all the Iron Daggers you crafted using the Petty Soul Gems. This will level Enchanting very fast.
6) Sell enchanted Iron Daggers to Adrianne, SAVE GAME, kill her, LOAD GAME, repeat until all daggers are sold. If you still need iron to level enchanting, buy some each time before selling. You will actually come out ahead, even more so with lucrative enchants (Banish). You will make more of a profit if you use rings and necklaces to enchant, but I find that crafting daggers is faster due to the ease of buying the mats.