In order to make sure you can recover your progress in the event of having to reinstall the game or switch devices, you should make sure to connect to a Game Center account.

You can connect by simply going to the in-game settings menu and pressing on the "Connect" button next to the "Game Center" option at the top of the window. At this point, you'll just have to log in with your Game Center account in order to finish connecting.

At any time after this you can recover your progress if you lose it by simply reconnecting to Game Center once again in the settings menu.