When you have available updates for your apps you will notice a badge next to App Store.
Run the App Store app on your device and go to the Updates tab.
Find the game in the list of apps and tap the Update button against it or allow all to update (you may have multiple updates available for other apps).
NOTE: Please read the update notes for each app before updating!
Please wait until the update is downloaded.
Done! Now you can play the game.