To save your progress, you need to have the app installed on your device and have the Apple Game Center app (the app is a standard part of iOS).
To save your progress:
- Tap Settings in the top right corner.
- Tap Login.
Your account progress will be saved in the Game Center.
If you reinstall the game or use it on a new device, you'll need to repeat these steps to load your saved account. The device must be logged in to the same Apple ID account with which you connected your main account.
After choosing your e-mail address and tapping the Login button, a window with a choice of accounts opens. You then have to choose which account you want to use on this device. The account you do NOT select will be overwritten.