Really you have two options here:
-
If your printer is not too new, then you can simply use HPLIP from MATE Welcome in Getting Started → Post Installation → Drivers → Printers:
Note: if you want, you can install it with APT by executing
sudo apt-get install hplip hplip-gui
. -
If your printer is new, then you have to install binary HPLIP.
You can follow my Q&A on AskUbuntu for details -