There are several ways to upgrade your gear:
1. Level Up - to level up your gear, you need a certain amount of Dust. Dust can be obtained by completing quests. You can also gain Dust from reaching some Ascension levels or can even earn experience points after using your gear in battle.
2. Infuse and Auto-Infuse- to use this option, you need duplicates of the gear you wish to infuse. The infused gear will have extra boosts. You can either infuse your gear manually or let the infusions happen automatically now!
3. Open chests - sometimes opening chests will level up some of the gear items you own.