If you were previously logged in with Facebook on Multiplayer and Tournaments, you can recover your progress by logging in with the same Facebook account on both playing modes. To recover your matches in Multiplayer, tap on "Play with Friends". To recover your progress in Tournaments, tap on the Level bar, and then, "Link to Facebook".
Your purchases will be recovered through your Apple/Google ID if you download the game with the same account and tap on Restore at the end of the in-game Shop.
If you do not have a Facebook account, your game progress is saved in your device's internal memory.
BEWARE: If you do not have a Facebook account AND change your device, you will lose ALL your progress.