The HP DeskJet 3320 is supported with HPLIP 0.9.7 which is included with ubuntu. I have verified that it was included with the HPIJS 1.3 release (which was a long time ago). Also keep in mind that HPLIP 0.9.7 is terribly old...*nudge* -- No driver for hp deskjet 3320 https://launchpad.net/bugs/34591