Build at least one valid house
Make sure the house has walls, a light source, a table or workbench, and a chair
Make sure the house is not corrupted, crimson, or hallowed
Have at least one gun or bullet in your inventory
Wait for the Arms Dealer to move in during daytime if the house is available
If he does not appear, keep the house empty and valid until he spawns
Buy guns or ammo from him once he arrives