You probably won't be able to explicitly password protect anyone for printing. What you can do is create users who need to logon, and those users will have a password. You can then add those users to the allowed users via the security tab for your printer, as explained in the answer above. Be sure to remove "everybody" from there, as well. The same users will have to exist on the other PCs on the network.
If you are a member of a Windows Server Domain, you have more possibilities to allow and restrict access to resources on your network, but if your not a domain administrator you will have to get into contact with your administrator.