The game automatically saves your progress every 5 minutes. Important events that occur in-game such as completing quests also trigger the auto save feature.

If you turn off the "autosave often" feature, which is only on the main screen options menu, the game autosaves every 20 minutes, in order to help improve performance.

You can also manually save your progress by clicking the gear icon between the Badges icon and the Coins display. Select either "Save and Continue" or "Save and return to Main Menu" to manually save your progress.