There does not appear to be a way for me to join groups, other than the Open Lounge (which I think I was auto-added to upon registration.) I do not see a status indicator on the right, as indicated in this guide, nor is there an option to join the group — the only option (available through the … menu) is to report the group.
I would guess this is true of almost everyone who has signed up, given the membership totals of the different groups. Is there an additional step in registration/verification? A waiting period before you can join public groups freely? If so it should probably be mentioned in the guide as well.