An item needs an enchantment slot in order to add an enchantment (which should start showing up on equipment about level 10, or so). If the equipment already has an enchantment, you need to remove it before you can add a different one.
In the equipment list it indicates which items have enchantment slots, how many there are and how many are filled (for one empty enchantment slot there is a '(0/1)' after the name; for 1 enchantment on an item with 2 slots, it shows '(1/2)', etc, and if there are no enchantment slots there is nothing after the (grey) name).