How do I hook up a printer so I can print with my iphone?

Have you gone to HP's website and set your printer up that way? I have the HP 5510 Printer and I can print from my iPhone with it. Its just using my home's Wi-Fi signal that I set up through HP's site. You might be able to do it right from the printer's screen too.

I cannot figure out how to get my AirPort

Extreme to recognize an HP Photosmart C4480 printer is plugged into the Airport Extreme USB port.

Assuming that other Macs and computers can print to the printer at the present time......you will need to install an App like Print Central on the iPhone to allow printing from that device.

PrintCentral for iPhone/iPod Touch - iTunes - Apple

Hi,

Plugging a USB printer to time Airport base only provide printier sharing to computers (Windows and Mac), not to iOS device.

The C4480 only provide USB connectivity and not supported by any iOS solution as AirPrint or the HP ePring app...

As suggested above, Print Central can do the trick by sharing the printer through your computer.

A couple of things come to mind. First did you set up the printer in your Airport Utilities? Is the printer USB only or is it also WiFi? HP has an App to control HP printers.