Open the app and open the main menu tray by tapping the hamburger menu below:
Tap Device manager
If you have not connected to any StagesBikes before, tap the + button in the top right and the app will walk you through the rest and automatically update the firmware in the process of setup. If you already have connected to a StagesBike, select it from the My Devices list:
Wait for the app to connect to the bike (all 3 panes will be grayed out when the bike is not connected), then tap the Settings icon in the top right of the control page:
The firmware version is indicated in the General section, if it requires update, it will be marked with a red alert icon as pictured below:
Simply tap this menu option to see an update overlay, select Update on the resulting overlay and the app will start the update. You can view all StagesBike release notes here:
A progress dialogue will appear and the update should complete successfully:
The new version should be reflected on the settings page with a green checkmark, your firmware is now up to date!