Clash of Clans has itself no “real” Gift Cards like for example PSN gift cards, Xbox Live, Apple, Google Play and so on. Gems can only be purchased via the Google Play Store for Android users and via the Apple Store for iOS users.
Android Users:
1. You need to open the Google Play Store App
2. Tap on the menu and select Redeem
3. Enter the code and press Redeem
4. Now you can open the CoC App and purchase the Gems using your Google Play Wallet
For iOS Users:
1. Open the App Store
2. Tap Today, then tap your Apple ID icon
3. Tap Redeem
4. Sign in with your Apple ID
5. Enter the 16-digit code
6. Now open the CoC App and use your App Store balance to buy CoC Gems