1. Open up the App Store on your phone and then click the Profile/Account icon in the top-right
2. Next, press "Redeem Gift Card or Code"
3. Next, press "Enter Code Manually" and then type in your redemption code. You might be asked to sign into Apple again afterwards.
4. Once you have redeemed the app. Go back to your Account page and press Purchased.
5. You should now be presented with a list of apps. Your new app should be at the top of the list, however if you've redeemed it before, you might need to scroll to find it. Simply click the Download icon next to and the app should now be installed on your phone like a normal app.