Levels are increased by doing activities at a Kiosk, viewing exhibits in the Academy, and completing Quests! Some Quests and activities will award more XP and Coins than others. Please note that some Quests may not reward you with experience points (XP), but they do issue Coins.
Your current Level is displayed in the upper left corner of your screen, along with a progress bar that shows how much XP has been earned.
The Quest button in the upper-right corner can be selected to review your current quests and details about each task.