To process any pending registrations in private groups*, go to the Members pane by choosing Members from the Admin drop down in the upper right or click on the review registration button in the email you received. 

In the Members pane, pending members will be marked by an orange "Pending" in their status. 

If you want to review information contained in the registration form, click the member name to be taken to their profile.

Approve the member by changing their status from Pending to Member or Leader.

* Note: For groups that are public to an organization, members will not be marked as pending and will instead become a member immediately.