I do not see your HP printer listed on Apple's list of AirPrint compatible printers at <iOS: AirPrint 101>. Could there be another number for it, that might be on the list?
As far as I know, the iPhone and iPad only print through WiFi. If you can connect a non-AirPrint printer to Wifi, you may be able to print to it using a printing App. I suggest you download the free HP App, ePrint Home & Biz. It has limitations but should get you printing. There are other printing Apps with more features, but they can only be accessed from within other Apps that have the "Open In" option.
Another alternative is to share your computer's printer as AirPrint over WiFi. Programs that can do that are Printopia and FingerPrint, and are reported to work well. Your computer must be on and awake any time you want to print. <Printopia for Macintosh> <FingerPrint for PC and Mac>