Game Center account connection is only available on Apple devices. If you also want to use Android devices, Facebook connection is the best choice.
All you need to do is click connect, either in the title screen or in-game settings, and select the Game Center option. If you are signed in to Game Center at that time, we will connect your Hideaway account automatically. If you are not signed in at the time, you will be prompted to do so.
If you are having problems authenticating your Game Center account, exit the game, go to your iPhone or iPad device settings, find the Game Center settings, log out and back in to your Game Center account, and re-enter the game. Sometimes the device can get confused about the device level authentication, and this often fixes it.