Some HP printers can use one of the drivers already installed by default in Ubuntu. In those cases, all you usually need to do is plug your printer into your computer, and Ubuntu will recognize it and prompt you to set it up. It’s super quick & easy. The HP Laserjet P1005 that I purchased needed something more. This is a good quality, small, quiet, and cheap ($75 shipped from Newegg) monochrome laser printer. It comes with drivers, Windows drivers of course, which do you no good with Ubuntu. I read that I needed hplip. Turns out that I already had hplip installed on my system by default (which will work for many HP printers), but it didn’t do me any good. I needed to download & install the newest version. Here’s how I did it…
Download the automatic installer file here, the sourceforge page for hplip. Once downloaded follow the instructions on the download page to complete the installation. It will download some more stuff, and then install everything. It will also configure your HP printer. Now you’ll have the HP Device Manager in the Accessories menu, and you’ll also have nice, smooth printing.

Source: http://howto-ubuntu.net/how-to-set-up-hp-printing-on-ubuntu/