Before you can use the google groups module, you must register your website as an allowed web application using the Google APIs Console.
Log in to your google hosted domain as an administrator and then visit the Google APIs Console.
Click on "Services" in the left column
- activate access to the "Google Apps Groups Settings API".
Click on "API Access" in the left column
Click the button labeled "Create an OAuth2 client ID"
Give your application a name and click "Next"
For "Application type" select "Web application"
Click "Create client ID"
- Provide all the necessary information.
Under "Simple API Access" click "Create new Server key..."
- Provide the IP addresses of your live Drupal site (and any dev or test sites as necessary)
* Fore more information, please see the Google documentation
