You can join the AHA when you register your entries online. That's probably the easiest way to do it and take advantage of the membership discounts immediately.
Just go ahead and register your entries like normal. Skip the field where you enter an AHA number as you register for the site. After all your entries are added, go to Pay for Entries. Just before you're asked for payment information you'll be offered a chance to lower your entry fees by joining the AHA. It's all done automatically and you don't need to wait for your order to be processed by the AHA Member Services Team.
Here's the link to register your entries: http://www.brewingcompetition.com/NHC/nhc.php
If you have problems, email me directly: Kathryn@BrewersAssociation.org