In many cases, Triple Town will automatically connect to Game Center. However, in some cases you must do so manually. Please follow the screenshots below to do so:
1. Sign in to Game Center if you haven't already done so:
Note that after Step 3, you will sometimes get the message below rather than what is shown in Step 4:
If you receive the message in Step 4a, first exit the game. Then launch the Game Center app and sign into it. Finally, return to Triple Town and repeat Steps 2 and 3 and you should see the screen change as in Step 4.