Basic Anvil: Drag a resource in to upgrade that resource.
Bronze Anvil: Drag a tier 1 defense in to upgrade that to bronze.
Silver Anvil: Drag a bronze defense in to upgrade that to silver.
Gold Anvil: Drag a silver defense in to upgrade that to gold.
Anvils can also be used inside your inventory, to upgrade something that's inside your inventory.
Pixel art credit to Daniel Eddeland. Art edits by NOMAD.