Hi Steven - the clans are open to all AVF members, and organised by whoever has set up the clan itself. If you check out my sig, there's a link to the full list, with the clan tag and clan organiser/leader and a link to the discussion thread (if there is one).
First thing to do is check out the discussion thread, introduce yourself, and make sure it's still active, then pop a friend request to the clan tag. Let the organiser know you've done this so they know to log in and accept you, or you could end up waiting a while.
Once you've been accepted, the clan tag will show on your friends list, where you can select it, move right to the Bio page and select "View Friends". This shows everyone else on the list and from here you can obviously see what everyone is up to. If you're setting up a party with the NXE, send out party invites and you may find some people will join you, or if you see someone already has a party going, see if you can join that one (not sure if you can join someone's party automatically if they aren't a friend directly...hmmm).
The idea of the tags is you can see AVF members who have that game too, or play at a certain time, or are just n00bs so you can match with people of similar skills & games. Don't be offended if people don't join your parties - they may be doing something else - in the same way don't feel you have to accept every invite that comes your way. Soon enough, you'll have met up with a few like-minded peeps.