The 5 Stages
Each base Relic Weapon can be upgraded four times before Trial of the Magians. Three of these four upgrades are handled by a Goblin NPC named Switchstix, who can be found in Castle Zvahl Baileys. Each of these three upgrades requires that you simultaneously trade him your current-stage Relic Weapon along with whatever materials he asks for. Switchstix will then ask for his commission in Ancient Currency; this is a separate trade, and the upgrade process will not begin until he receives it. Your Relic Weapon and materials cannot be returned once traded.
Furthermore, no other upgrades can be performed until the Ancient Currency commission has been traded to Switchstix. Time needed for the upgrade process varies by stage; when the waiting period is over, speak to Switchstix again to obtain your upgraded Relic Weapon. The specifics of this process can be found below.