To play your game on a different device you can log in to Facebook, Google Play, or Apple account to load your previously bound game (you must bind your game first before you can load it).

When you log in to your account, you'll have an option to load two different games, each displaying your in-game nickname and level.
The two accounts should be the one currently on the device and the one bound to your account.
You will need to confirm which one you would like to load.
Once you've chosen a game, another window will appear where you must type the random verification code.

Take note that after tapping on Replace, the other game data will be deleted and cannot be recovered, unless it is bound to another account.