Expanding your house and upgrading your sword are two completely different things. I'll answer both.
To expand your house, James sells house expansions and crafting expansions on Thursdays and Holidays between 12 PM and 6 PM.
To use the forge in the blacksmith interact with the little triangle interaction thing near the anvil, which is behind the counter. This will open up the forging craft screen, but the forge at the blacksmith only allows use of up to 2 ingredients. You have to get a Advanced or Master Forge in your house to make up to 4 or 6 ingredients (respectively.).