For Android devices:

Open Google Play Store.
Tap the Menu icon in the top left corner, and then My applications and games.
Find the game name in the list and tap it.
Tap Update when the game page opens.
You can also adjust your device settings to automatically download updates for the apps you have installed:
1. Open Google Play Store.
2. Tap the Menu icon in the top left corner.
3. Go to the Settings section.
4. Tap Auto-update apps.
5. Choose one of the following:
- Auto-update apps at any time. Updates will be downloaded via both Wi-Fi and your mobile network.
- Auto-update apps over Wi-Fi only. Updates will only start downloading when your device has a Wi-Fi connection.
 
For iOS devices:
Open the App Store on your device.
Tap the Updates icon on the bottom panel.
If a new update is available for the 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.