You can use various Cloud Services to make sure your progress is safe:
• Google Play (Android only)
• Game Center (iOS only)
Both options require you to set up and sign into a valid account with the respective service.
You can find the option to connect your game in the in-game options menu. Make sure the corresponding button is colored green and your progress should be saved in the cloud.
If you should lose access to your account or wish to play on a new device, you should be able to recover your account after a certain point in the tutorial. As long as you use the same Google Play/Game Center, you should be presented with the option to load your original account from the cloud.