This facility is unlocked after completing the quest “Forge the Way” on 8/10. The Blacksmith can be conveniently accessed from the Marketplace option in The Calendar or during the Battle Preparation screen. While exploring, you can also visit the Marketplace on foot and visit the blacksmith there. Regardless of how you access the Blacksmith, there are two options that you can choose from this facility.
Use Smithing Stones and corresponding fee to completely replenish a weapon’s durability. Later on, the Sword of the Creator can be repaired as well but will require Umbral Steel instead.
Spend Smithing Stones to completely replenish the weapon’s durability and permanently increase it’s max durability. The weapon will also have a “+” suffix on its name. Forging a weapon is basically upgrading it so more Smithing Stones and gold will be required.
You can also Forge a broken or rusted weapon. A broken weapon will be treated like a normal weapon when forged; it’s Durability will be replenished and its max durability will be permanently increased. Rusted weapons on the other hand, will be turned into an ordinary weapon (usually iron)
Smithing Stones and Black-Sand steel can be purchased from the Eastern Merchant in your Marketplace once you've unlocked him. Umbral Steel can be obtained as quest rewards or when you break seals of powerful beasts you’ll encounter later in the game.