From Moodle News by Joseph Thibault
Jérôme Mouneyrac has updated perhaps the most robust authentication plugin for Moodle which supports 7 different authentication sources including Facebook, Google, and LinkedIn adding a very simple and easy registration option for new users on your site (if the site is open to self-registration).
The posted installation process looks both simple and easy to follow (just three steps). Once installed choose which Auth options you want to employ on your site.
Download it here: https://moodle.org/plugins/view/auth_googleoauth2