There are currently 3 different ways to save your game progress and resume it if you change to a new device.

If you're using an Android device, then you can link your account with Google Play. If you're using an Apple device, Apple ID will help you save your game.

The login save method available to all devices is Facebook. You can read more about it HERE.

Note that if you don't login with any of those you can't resume the game on a different device.