From the social area (the 4 faces talking icon) you should choose the "connect" option along the bottom, followed by "connect" under the Apple ID icon. You can use Apple ID to log in to a game from the main menu, and you will be able to log in to your game on any other Apple device you have with the same Apple ID.
Please be aware your game can either be linked to Apple ID or Facebook, but not both and trying to link an additional method will not work.