Does your printer have a network cable connector? If so, it can plug directly into your router, and using "Network Neighborhood", you can see the printer (as well as both computers). On both computers, you'll need to open the Printers Control Panel and add the networked printer to both of them. In this setup, you only need the printer and the computer you wish to print from turned on in order to work.
If not, connect the printer to one computer and install like normal (as a Local printer: it's directly connected to that PC). Then, right click the printer in the Printers Control Panel, choose Sharing, then give it a name on the network. It'll take a few minutes for the network to recognize the new printer, then go to the other PC, open the Printers Control Panel, and add a new networked printer. (Don't choose "Local" on the networked PC.) In this setup, you'll need to have BOTH COMPUTERS turned on and the printer turned on for the networked PC to be able to print.