Purchase the plugin on the Official Unreal Engine Marketplace.

In the Epic Games Launcher, the plugin will appear in your Library.
Go to the Library tab and find the plugin and add it to the engine.

In Unreal Engine, the plugin will be available in the plugins section.
Go to Settings -> Plugins -> Search for "Play Services Billing" and ensure it is enabled.

Other plugins or software upgrading the Billing Library for you can cause issues or even override this plugins update.
Go to Settings -> Plugins and disable any other custom Billing plugins you may have purchased off the Marketplace.

Add your "Google Play License Key" from the Google Play Console.
Go to Project Settings -> Android -> Google Play Services and fill in "Google Play License Key".