I don't have that exact printer but here is how to install printers.
1) Click Control Panel on the mintMenu
2) In the Control Panel, under the Hardware section, click printing.
3) At the top of the window that opens you will see a button that says. "New Printer"
4) In the New Printer window you should see your printer as the first option on the side panel. Click Forward
5) It should automatically select Hp so just click Forward again.
6) Find your printer in the list on the side, (I don't see it so I would use the next highest number, so 1400 probably.
7) Change information about the printer if you care
Close everything and print.
That should get you going, Hope that helps
P.S. The picture is a little bit on the questionable side.