What a pain. If you go to the HP web site and enter the HP Laserjet 1020 as your printer and then pick Windows 7 64-bit for the OS, it gives you drivers that it claims are compatible with Windows 7 64-bit. Not so.
The drivers are actually for Vista 64. The z-7 zip file complains that it won't run on a windows 7 64 bit machine and to contact the vendor. So you end up having to use winrar to extract the files. Then when you run setup.exe, you get a similar message that says it's not compatible with Windows 7 64-bit. Very frustrating, since HP offered the driver as a solution for Windows 7 64-bit. And yes, I submitted feedback on their web site.
Finally, I used these instructions on HP's forums that helped a lot. See: http://h30434.www3.hp.com/t5/Printer-All-in-One-Install-and/install-HP-Laserjet-1020-printer-Driver-windows-7/m-p/145921.
Be sure to check the video links for a better explanation. The opening instructions has a lot of assumptions. I did my install all from devices and printers and there was no install driver from specified location option. I used the troubleshooting option which worked to reinstall the drivers. On my system, it had been working. I don't know if the customer moved the usb cable to another port or what reason it suddenly disconnected itself from the system. I had a printer driver that indicated it was working, but wasn't and a HP 1020 unidentified item on the devices and printers screen.
I removed the HP 1020 printer and went into print server properties and removed the driver as well. Then I right clicked on the unidentified icon and selected troubleshoot. The trouble shooter found the driver and installed it again and it worked.