Enchanting is a mix of using known runes, your enchanting skill, weapon quality, and material.
The most basic thing to create an enchant is to escribe known runes something that you wish to enchant by carving them into the item, or if a higher level, transcribing the enchant onto something (needed for rings, amulets, and most jewelry). These known runes are gotten from enchanting shops, ruins, or found almost anywhere in dungeons.
Enchanting skill allows for a chance at higher level enchants and a higher chance for success.
Weapon quality allows for a chance at higher level enchants similar to enchanting skill, however if your weapon quality is below Average, you are hard-capped to normal level enchants.
Some materials allow for a higher enchanting efficiency and can make higher level enchants more common, these materials include Silver, Gold, Etc.
Soul gems are required for enchanting, as well as a certain amount of mana.
Some enchantments require higher level soul gems, and a minimum amount of mana.