Connecting your game to Google Play allows you to save your progress after deleting or re-installing the game. You'll also be able to use the same account on different devices.
1. Open the Google Play app and log into your Google account.
2. Go to Game Settings (the "⚙" icon in the top-right corner) and open the "Account" tab.
3. Tap the slider near the Google Play Games icon.
4. In the window that opens, choose the Google account you want to use.
Now your progress is saved in Google Play!
Please note: only one game account can be connected to one Google Play account. Connecting multiple accounts will lead to progress being lost on one of the accounts.