It is easy!
You can save your progress by linking the game to your Apple ID or Facebook account.
You can do it directly from a game Title screen after you launch the game (recommended).
 
 
Оr you can do it later by using game Settings menu. 
 
 
Please note that without linking to Apple ID or Facebook acсount you can still play the game using Guest Account, but your game progress will be saved only for a current device you are using, and will be lost if you launch the game on a different device. 
 
Linking Apple ID or Facebook account from the game Settings menu.
 
In order to save your game progress using your Apple ID, please do as follows:
  1. Open game Settings (with ⚙️ icon on a main ingame screen);
  2. Go to "Account" tab;
  3. Press "Link";
  4. Choose Apple; 
  5. It's all set! Now your game is linked to your Apple ID, and your progress is safe.
In order to save your game progress using your Facebook, please do as follows:
  1. Open game Settings (with ⚙️ icon on a  main ingame screen);
  2.  Go to "Account" tab;
  3. Press "Link ";  
  4. Choose Facebook;
  5.  It's all set! Now your game is linked to your  Facebook, and your progress is safe.