Welcome to LinuxQuestions.org. Based on your description, it is likely the configured driver is not suitable for your printer, or some other problem exists within the filter chain. We can examine the CUPS error_log for further information if need be, but to start with examine the ppd file to show which driver (filter) is currently in use...
Code:
egrep -i "name|model|filter" /etc/cups/ppd/*
The output can be posted here if help required to make sense of it.
1) The openprinting.org site lists the foo2zjs driver as being suitable for this model
http://www.openprinting.org/printer/HP/HP-LaserJet_1020
More info about installing and configuring with this driver...
http://foo2zjs.rkkda.com/
2) Alternatively, you can use the HPLIP driver
https://developers.hp.com/hp-linux-i..._devices/index
Install the hplip package from your distros repository and set up using its installer...