You can use the Facebook's API to connect your users to your site using their Facebook account.

If the registration is closed, the user will be allowed to login if the email address already exists in your database. 


The first thing you want to do is to enable the Facebook Signing through the Theme Settings > Login / Register > Facebook Options:

You will now need to create a new Facebook App for your site from this page: https://developers.facebook.com/apps/


Finally, you need to copy/paste the App ID and App Secret back to the Theme Settings and save everything.


Facebook has also several settings that let you customise the Application page, such as the logo and content.