1 - First of all bind you main game process to your main Facebook or Google account on your old device.
2 - Download the game on your new device: a new game process will start automatically.
3 - Login your previous Facebook or Google account on the new device.
4 - Follow the tutorial until the end.
5 - Go to settings, and then you will be able to switch to your old account under the option 'Switch Accounts'.
6 - Choose Facebook or Google to switch back to your main game process.