HP Printers (and others) not on compatibility list and Airport Extreme or Airport Express Printing using 10.4
If an HP printer (or other printer) is not on the unofficial compatibility list this generally means that it is not supported for use with the Airport Express/Airport Extreme Base Station with the vendor's own printer driver and may not work at all.
It may work with a third-party driver such as the HPIJS drivers or the Gimp-Print drivers, but this is not the case with all printers.
This guide is for 10.4, please follow this guide if you are running 10.3.
Open Printer Setup Utility in the Utilities folder in Applications.
You will now be faced with a new window (you may already have printers listed).
Click the Add button.
When you start Printer Setup Utility to the right of Default Browser in 10.4 is an icon called IP Printer. Click this icon.
If necessary change the dropdown box from Rendezvous (or USB or whatever) to IP Printing.
You should now see this window.
Change Printer Type to Socket/HP Jet Direct.
Add the IP address as 10.0.1.1 (assuming your Airport Express is at its default IP address).
Select the relevant HPIJS or Gimp-Print Printer Model.
Note this HP Page if you have a HP PhotoSmart or All-in-One printer.