Unlock the Blacksmith to gain access to the Forge. In the Forge, you can improve any item, unless the item has already reached its maximum level. Improving an item level increases the stats of any Weapon, Armor or Banner.
Use a specific number of Ingots of the same rarity as the item you want to upgrade to the next level:
At certain intervals, you can't upgrade your item any longer, before it has been reforged to the next rarity tier. The process is identical to upgrading, requires reforge Cores rather than Ingots. Use the required number of reforge Cores from the next rarity tier to reforge an uncommon item to the rare version of it, for example.
Upgradable items have an indicator in the form of a small, green + icon: