In The Elder Scrolls V: Skyrim for the PC, PS3, and Xbox 360, just like in previous versions of the game, you can enchant items and weapons to make them much better and more useful than they would be otherwise.
Enchanting is quite a bit different in Skyrim, in that you now need to disenchant items to gain enchantments. Disenchanting, enchanting, and even recharging your weapons all increase your enchanting skill.
A good way to increase your enchanting skill quickly is to enchant cheap weapons and armor with petty soul gems. It seems that the size of the enchantment doesn’t effect the skill gained, so smaller soul gems are you best source of leveling.
Follow my guide to make a lot of Iron Daggers with smithing, or just keep your weapon loot from dungeons, and enchant them using filled soul gems. The best return for enchanting is the Banish enchant, which banishes Daedra. The Banish enchant can literally turn an iron dagger from being worth 10 gold, to well over 1000 gold depending on your bartering skills. Using this method, you can purchase all of the soul gems from the mages you encounter, and pretty much buy your way to high level enchanting.
To fill your soul gems naturally, use the Soul Trap spell, or enchant a weapon with the Soul Trap effect. You can find the Soul Trap spell from most spell book vendors, and the Soul Trap enchant can be found fairly easily on most weapon vendors. The mage at Dragonsreach in Whiterun typically sells the spell book.
One method that will help with this process immensely is to get The Black Star item. The Black Star is a soul gem that can trap any size of creature, and it is never broken or consumed when you fill an item with it, essentially giving you infinite grand soul gems.
To get The Black Star, you need to start the quest by the same name. Speak to Araneas in the Shrine of Azura, which is in the mountains directly south of Winterhold. Once the quest is complete, you will have the choice to return the broken Azura’s Star to Araneas or to a man named Nelacar. Returning it to Nelacar will yield The Black Star.
Once you have The Black Star, it can be filled indefinitely with any sized soul. You can then use it to create and recharge any number of items, taking some of the burden off of buying soul gems.
The Black Star makes a perfect infinite recharge gem, since you can fill it, recharge your weapon, and fill it again multiple times all in the same dungeon.
If you’re ok using a rather “cheap” method to level Enchanting extremely fast, then check out the first tip in my skill trainer pickpocketing guide where you simply find an Enchanting skill trainer, buy a skill point, then pickpocket the money back. Hamal in the Temple of Dibella in Markath, and Sergius Turranius at The College of Winterhold are both Enchanting trainers.
This trick is only effective up to 51 skill points unless you have a pickpocketing skill of 100, since after 51 skill points the cost is increased by 1000 gold, making pickpocketing much more difficult.