If you don't have anything equipped in the equipment slot, and the item is of the appropriate level, it will be automatically equipped for you. However, if you need to manually equip an item, tap your portrait in the top-left of the screen to enter the Character Menu. Tap the Equip icon (the sword-and-shield) at the bottom-left to enter your Equip Screen. From here, you can tap any of your equipment categories to view your currently equipped items. To change an equipped item for another, tap the Change button, tap the new item you want to equip, and then tap the Equip button to confirm the switch.