Go to your System Preferences, then to Print & Fax
Is your printer listed there?
Is the printer turned on?
Check in the Apple Menu/About this Mac
Click on More info from that window, which will open your System Profiler
Click on the USB tab from the list.
Is your printer listed there? If not, recheck that it is both turned on, and that both ends of the USB cable are plugged in firmly.
Press Command-R to refresh that device list. If your printer appears there, that's good...
RESTART your Mac.
Return to your Print & Fax pane. If your printer now appears - Go to your Apple menu, and choose Software Update.
Install any update for HP printers that show there.
Or, alternatively:
Download and install the full HP driver set that Apple supplies.
It's here:
http://support.apple.com/kb/DL907
If the printer appears in the pane, but just doesn't seem to print properly - remove the printer from the pane, and re-add it.
on an unrelated note:
I've got a picture of my kids sitting on the back of a jackalope at Wall Drug. You wouldn't know anything about that, right?