If the printer is directly connected and installed via USB/LPT1 on one PC, any other PC that wants to connect to the printer will need to be able to authenticate to the first PC. This means authenticating as a local user on the first PC. You will need to create a user account on the first PC with the same username as the one you login to the 2nd PC with, with the same password.
After that, it is best to uninstall the printer, browse to the first computer in Windows Explorer by entering in the address as \computername\, and then right-clicking on the printer, and choosing Connect.
If the printer is connected to a router by ethernet, you won't have to first authenticate, unless security has been set up on the printer.