Most soul gems start off empty, and must be filled with a creature's soul before they can be used. They come in a variety of sizes: larger soul gems can hold the souls of more powerful creatures, which yield stronger enchantments. You can find soul gems throughout the world, and buy them from many merchants. Once you have learned an enchantment, you can use it to enchant any number of items. You can learn enchantments by disenchanting (destroying) enchanted items at an Arcane Enchanter.
Enchanting an item requires three things: an enchantment, a filled soul gem, and a weapon or piece of armor that does not already have an enchantment. Use Arcane Enchanters to enchant or disenchant weapons, armor and some jewelry.