I got an HP LaserJet 1020 via USB working today with Linux Mint 17.1.
I went to the hp support page for drivers for the 1020 and selected Linux and follow the dialogs to select the distribution. I was told that HPLIP (HP Linux Imaging and Printing driver) is already included with the Linux Mint distribution.http://h10025.www1.hp.com/ewfrf/wc/soft ... ct=439320&
I clicked to download the driver anyway, and got sent to the HPLIP website where I downloaded the latest version of hplip.http://hplipopensource.com/hplip-web/in ... index.html
Following the instructions on that page, I ran the driver installer, entering the defaults to all of the prompts. Near the very end of the installation, the installer ran hp-setup, a gui window and I saw a message that said that something like "An additional driver plugin is required to operate this printer". The installer offered to download it for me and install it, so I selected OK. Once the plugin was installed, suddenly the printer came to life and I was able to print a test page.
After that, the printer worked great!
The installer also installed an hp status program that shows an icon in the notification area of my launcher panel. It is much nicer that the status info that is included with the distro printer setup.
I probably could have run hp-setup from the start and skipped the download and install of an updated HPLIP, but that's what I did anyway, and it now works.