Your game progress is saved automatically if you are using the Google Play Games app and your device is connected to the internet.
Please note that Facebook does not support cloud synchronization for this game and therefore cannot allow you to store progress.
If your game progress is not synchronized with the Google Play Games, on the loading screen there will be a pop-up window. It will suggest turning on synchronization with Google Play Games. Choose "Allow". After that the progress will be stored in the cloud. This will allow you to restore your data in case you reinstall the game, change devices, etc.
In case you have several Google accounts you can manage them and choose the one you wish to use in this game. This window appears if you turn down previous offers.
You can always turn synchronization on manually from the options of the game.
In case you have not turned on auto-synchronization in the options of Google Play Games, you will be offered to do this on the loading screen of the game.