The Anvil is used to combine items for crafting Melee gear, Archery gear, Magic gear and Enchanting.  Equip your Forging Hammer Forging Hammerand click on the Anvil. Have the proper ingredients in your inventory and a selection of items you can make will be shown. Select the one you want and 'Make' with an associated percentage value will appear below the picture of the item to be created.
Anvil Forging

Crafted items can also be Recycled with a 50% chance to get back the ingredients and half the experience per item returned. You must have the level to craft in order to recycle.

Anvil Recycle

Formulas shows a searchable listing of all items that can be made at the Anvil sorted by crafting skills for Forging, Wizardry and Fletching. Search by item name or any single ingredient. Partial names accepted.

Anvil Formulas
Enchanting is done at the Anvil using the item, enchant scroll and up to three Orbs of Luck adding a 10% chance to enchant per orb used.