@ Deafmute: Enchanting works like this - you need 3 things: first, an item to be enchanted, second you need to know an enchantment to cast on the item and third you will need a filled soul gem.
1) This can be anything worn or wielded by your character, but the hidden "item level" determines what kind of enchants it can take. Don't expect a random Hide hat to take the same kind of enchantment as a Daedric helm.
2) You need to learn enchantments by finding magical items and then destroying them at an Arcane Enchanter. The level of the enchant on the item is irrelevant, only the effect, so for example if you find a dagger that has a "absorb 1 health" effect on it, you can later with the correct soul gem make a dagger or mace or bow that absorbs 20 health.
3) Soul gems are containers that have the soul of someone or something in them. To capture a soul, you need some way of casting "Soul Trap" on the target, either the actual spell or using an weapon enchanted with Soul Trap to land the killing blow, and of course an empty soul gem. Souls range from Petty souls of foxes and wolves all the way to Grand for the strongest monsters. An exception to the rule is if the creature is sentient it will always have a Black soul, regardless of how powerful it is, in that case you can only store the soul in a Black soul gem. Black and Grand soul gem shatters after you use them, the others do not, but otherwise Black souls are functionally identical to Grand souls. Creatures with Grand souls are extremely rare, but you can get Black souls off any bandit or beggar, which brings us to...
4) There is a really quick and easy way to get a unique artifact, Azura's Star, which is arguably the most powerful item in the game which will let you ignore the whole Soul gem system. Basically, it is a re-usable Soul Gem that can hold either a Grand or Black soul in it (you need to choose when you get the item, and the choice is permanent). Since Black souls are all over the place, you should choose this option. To get it, simply talk to a bartender until you get a rumour about the Shrine of Azura. Go there, talk to the chick, she sends you to talk to the elf in Winterhold, go to the dungeon he tells you about, get the Star and then return to the elf. He does some magic, you defeat the boss and you will have the best item in the game. Your enchants will now be extremely powerful.
@Nanaki: unless you store items in a container within a house that you own, stuff will randomly disappear every time you zone in or out. I recommend doing the main quest until the point (very early on) where you can buy property in Whiterun.