Use Arcane Enchanters to enchant weapons and armor. 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.

You can learn enchantments by disenchanting (destroying) enchanted weapons and armor at an Arcane Enchanter. Once you have learned an enchantment, you can use it to enchant any number of items.

You can find soul gems throughout the world, and buy them from many merchants. They come in a variety of sizes: Larger soul gems can hold the souls of more powerful creatures, which yield stronger enchantments.

Most soul gems start off empty, and must be filled with a creature's soul before they can be used. To fill a soul gem, cast the Soul Trap spell on a creature and kill it before the spell wears off. If you have a soul gem of the appropriate size (or larger) in your inventory, the gem will absorb the creature's soul.

Any weapon enchantment can be applied to any weapon. Select the weapon you want to enchant, the soul gem you want to use, and then the enchantment. A slider bar allows you to select the power level of the enchantment. Stronger enchantments consume more charges per hit, which mean you will have to recharge the weapon more frequently.

Some armor enchantments can only be applied to specific pieces or types of armor. Select the armor you want to enchant, then choose from the available enchantments, or vice-versa. The soul gem you use determines the strength of the enchantment. Armor enchantments are permanent and do not need to be recharged.

ENCHANTED WEAPONS

You can find enchanted weapons in the world, or create them yourself at an Arcane Enchanter. Enchanted weapons use up soul energy with each successful hit and need to be recharged when drained.

To recharge an enchanted weapon, select it in your inventory and press the recharge button. Then select a filled soul gem from the list to recharge the weapon with it.

SOUL GEMS

Soul gems are stones that can store the souls of living creatures. Filled soul gems are used to create and recharge enchanted items.

Soul gems come in different sizes. The larger the stone, the larger the soul it can store, although larger gems can also hold smaller souls.

To fill a soul gem, cast the Soul Trap spell on a creature, then kill it before the spell wears off. If you have an empty Soul Gem in your inventory that can hold the creature's soul, the soul will be bound to the gem. If you have several empty Soul Gems, the creature's soul will be stored in the smallest gem that can hold it.

Note that most Soul Gems can only hold the souls of living creatures. Only Black Soul Gems can hold the souls of humans. Undead, Dwarven Constructs, and some other creatures don't have souls you can capture at all.

The following are examples of soul gems you might find:
Grand Soul Gem
Greater Soul Gem
Lesser Soul Gem
Petty Soul Gem

RACES

The following races get a +5 starting bonus to their enchanting skill:
High Elf, Imperial, Orc

PERKS

To get the most out of your enchanting, you should consider the following perks:

ENCHANTING
Enchanter - This makes new enchantments stronger
Soul Squeezer - Makes soul gems provide more magicka for recharging of items
Soul Siphon - When you kill a creature you will trap some of the creature's soul, recharging your weapon in the process
Insightful Enchanter - Increase the skill enchantments on armor
Corpus Enchanter - Increases health, magicka and stamina armor enchantments.
Fire Enchanter - Increases strength of fire enchantments on weapons and armor
Frost Enchanter - Frost enchantments on both armor and weapons are stronger
Storm Enchanter - Storm enchantments on armor and weapons are stronger
Extra Effect - Lets you put TWO enchantments on the same armor or weapon

CONJURATION
Soul Stealer - When you strike a target with a bound weapon, it casts soul trap on it.