Summarize this article:

See external links below.   Examples include "hp LaserJet 1020 Series.pkg."  It is labeled as "hp Laserjet 1022 Series.pkg," but run it anyway.   If the printer does not show up on the Printer Setup Utility, you may need to select Browser on the same dialog box and click on the HP1020 name there.

Summary:
Turn off and unplug the printer. Download and install the latest HP Drivers. Go to the Printer Setup Utility and choose HP Laserjet 1022 1.3.0.261. Download . Go to /Library/Receipts and delete any files for the HP 1020. Go to the Printer Setup Utility and delete any files for the HP 1020. Run the DMG file. Turn on and connect the printer. Go to System Preferences > Print and Fax. Select HP LaserJet 1020. Click add.