Enchanters disenchant surplus magical items - and use the residue to permanently augment equipment of their choosing. With the right incantations and materials, an enchanter can add bonuses to their armor or weapons, making them stronger, faster, or more resilient (among a host of other mystic powers). Canny enchanters sell their unique services to other heroes, and command prices commensurate with the rarity of the work they produce.
Enchanters need the residue of magic items to work - the more potent the item, the rarer the residue. They also require enchanting rods to channel their magic.
Enchanting doesn't rely on a particular gathering profession, so Enchanters occasionally pursue Tailoring to allow them to quickly create magic items to disenchant.
Make sure that you've learned the enchantment formula you'd like to use, and that you have the appropriate enchanting rod and the special materials required for that enchantment in your inventory. Some ingredients can be purchased from a trade goods vendor, but magic essences, the primary ingredients, are normally only found on the found on the auction house, or, more often, extracted from other items with disenchanting.
To extract a magic item's essence with disenchanting, simply choose the item you'd like to disenchant (it must be 'uncommon' quality or better), choose 'disenchant' from your professions menu, and click on it. The item will be consumed, and you'll receive magic essences to fuel your enchantments.
To enchant an item, first place that item in your inventory (if you're enchanting for another player, have that player place the item in the trade window). Then, choose 'enchanting' from your professions menu, click on the enchantment you'd like to place, and then click on the item you'd like to enchant!.