Rest at a bonfire
Select Modify Equipment
Choose the weapon you want to upgrade
Use the required Titanite materials and souls
Confirm the upgrade
For boss weapons or special weapons, use the Blacksmith
Find Blacksmith Lenigrast, Blacksmith McDuff, or Blacksmith Ornifex for special upgrades
Infuse weapons at a blacksmith if needed
Reinforce weapons up to the maximum upgrade level
Repair the weapon if it is broken before upgrading