Unless you sign into Apple's Game Center app, Tunnel Town can only save your game on the device you are currently using. Switching to a new device will mean starting the game over and creating a separate burrow. If you want to be able to access your burrow from multiple devices and see your friends in the Buddy List, you need to connect to Game Center.
If you choose to connect to Game Center, please do the following:
1. In Tunnel Town, click the Settings Button in the bottom right corner of the screen, and then click the "Switch User" button.
2. If you see a button with your Game Center name on it, tap it and it will load your burrow tied to that Game Center account.
3. If you don't see a button with your Game Center name on it, close Tunnel Town and open the Game Center app on your device.
4. Sign in to Game Center, and then open Tunnel Town.
The game will then load the burrow tied to that Game Center account.
If you have further questions about using Game Center or creating a Game Center account, visit this link for Apple’s Game Center instructions and support: http://support.apple.com/kb/ht4314