1. Open the  App Store  on your device. 
2. Tap the  Updates  icon on the bottom panel. 
3. If a new update is available for your game, it will appear in the list. Tap  Update  next to the update description to download it. 

You can also change your device settings to automatically download updates for the apps you have installed: 

1. Go to  Settings  ->  iTunes and App Store
2. In the Automatic downloads section, turn Updates on.