There's no extensive documentation for GJ at this time as it's still maturing and the documentation would likely change significantly with each release.

The invites work as any invite would. For example you invite a user by email address to a group. They then register with that email address and you can configure GJ to auto accept the invite or they can view Invited tab in their profile on the Groups tab to accept invites or they can browser to the group and click Join. If they're already registered to the site then the steps are the same except the registration process.

1. Another CB user invited my to his group. I got an email with as link. I clicked on it, but I was not logged on, so CB told me to log on. I did. I expected to see the "group successfully joined", but I did not. I had to go back to the invite email and click again. Then it worked.

Right, this is normal. CB can't redirect back to the invited link; it doesn't know where a user came from. You can also login, view Invited tab in your profile on the Groups tab to accept the invite or just browse to the group and click Join.

I would expect also that if someone invited me to as group and I was not logged on, then the next time that I did log on, I would be notified that I have a pending group invitation to acknowledge. Am I missing something?

Nope, there is no such thing. I assume you're wanting something similar to the new wall post or new PM notification in the login module. This is something that maybe added with a future release.

Please ensure you're using GJ 2.5.1. The invited tab was implemented with GJ 2.5.