Congratulations on the new Airstream!
You can either join WBCCI as a part of a unit, or a member at large. I think that joining through a unit will allow one to get a good deal more out of the club and would recommend that route unless you have a specific reason for wanting to not associate with any unit.
You can join WBCCI here:
Dues will be $55, plus your unit dues which can vary a good deal from unit to unit.
Save Wally has a terrific unit guide here:
SaveWally's Wally Byam Caravan Club 2009 Unit Guide
Which will provide you a great deal of information about the units so that you can make an informed decision.
Each unit is different from all the others, I would not worry too much about choosing 'the wrong one.' If you end up not enjoying a particular unit, simply change later, there is I think the perfect unit for everyone.
WBCCI also offers intra-clubs you can join, and one can be an associate member of a unit if the desire to join more than one is there.