Hi and welcome. First, as with any install of a new GNU/Linux system, Printer drivers aren't there. In the past printers would not automatically be discovered, but what happens now with the latest kernel/s is it recognises your make and model of printer, but if you look closely at the printers properties it states it is 'driverless' (I have covered this in the Unofficial Manual for Zorin 17).
Having recently migrated to a different OS and joining that forum I have discovered that there is a meta (not Facebook!) driver for printers. Install Synaptic Package Manager from Software, launch it (you will need your login password to run as 'root'), search for 'printer-driver-all'. This pulls in all packages concerned with printers, the crucial one being Gutenprint which has all up-to-date drivers.
The other point I make in the unofficial manual is that you should not use Menu | Settings | Printers to install a printer (I learned this from the now defunct PearOS forum). Open a terminal and enter:
sudo system-config-printer
This brings up the same interface as going through settings but ensures the best way to install your printer.
If you have used the sudo command it means your printer settings are unlocked to allow you to add a printer. I have missed this myself in the past as there is usually an 'unlock' button top right of Printers interface. Press this and enter your login password to unlock Printers to add your printer.