You may continue to play your game on another device as long as your account is connected with Google +, Facebook or Game Center.
In order to activate your account, run the game on your new device, then once you are in town go to ‘Settings > Account Settings’ and choose the account you were previously linked to (Facebook/Google +/Game Center). You can also choose to link your account as soon as you are done running through the tutorial. On the screen where you are asked to choose a name you will also be given the option to log in through a pre-existing account.
If you are switching from iOS to AOS or vise versa, your account will have to be synced to Facebook to transfer.