Group contacts allow everyone in your group to share an address book. One of the main reasons you want to be careful when adding random members to your group is that they can see and edit these, which is very dangerous in the wrong hands. If you have any somewhat sketchy, random people in your group, do not use this feature.

That said, you can access it from the "Group contacts" link on the right sidebar of the group. To add a new contact to your group database, simply click 'Add new contact' at the top of the page and a form will drop down. Fill out the form. Yes, the last name is required. If you don't know it, just enter "<unknown>" or a space or something. You can categorize them however you want (if you have ideas for new categories you can privatemessage nickb about them, but I'll only consider categories that would be useful to most other groups). Hit submit.

Now on the contact table you will see the first and last name, the time of the last note/comment, and a bunch of links with arrows next to them. Click any of these and stuff will load up and drop down.

View view all information about the contact.
Edit edit information about the contact
Browse notes view all the notes people in your group have posted about the contact
Add note add a new note about the person, eg 'this person said he's interested in volunteering to cook for our event next thursday'.