Your weapons can be upgraded in Remnant: From the Ashes. To do this you’ll need to visit a vendor in Ward 13 to make the upgrades. This NPC is located on the south side of the Ward 13 map that will upgrade your weapons and armor.
The Upgrade Station is located in Ward 13 near the world crystal
Simply return to them anytime that you have the scrap and materials to make the upgrades and you can do so. Weapons and Armor will both require that you have iron and scrap to upgrade them. The required amount and type of iron will be listed at the bottom right of the upgrade menu. The required scrap will be listed next to the menu item showing the damage stats.
As you upgrade weapons you will need more iron of better quality. Starting with Iron, working to Forged Iron, and Galvanized Iron. Scrap, however, is the same resource.
Weapons and armor can be upgraded multiple times, each time raising its power. Base weapons can be upgraded to +20, while crafted weapons from bosses can be upgraded to +10.
