You need to find and download the printer driver. Network printers have a connectivity procedure you must follow when installing the driver itself.
In the case where the printer does not need a driver to work, it should simply be available to print to.
I found that (depends on version of windows) add a printer> then select network printer> then as long as the computers can see each other on the network double click on the other computer and should show the installed printer on that then select it. That should work (does with XP) takes me less then 2 mins no drivers required. only thing is the other computer needs to be on when printing
If you have the install cd that came with the printer there is usually an option as to how you want to connect your printer and if you choose wireless and connect it to your router it becomes a network printer.
If now you want to connect your second printer by a switch then the printer has to have an ethernet port on it so you can connect it to the switch by ethernet cable. Once you have or find the drivers for the printer you can load them into the computers on the network and then connect the printer to the switch and in printers and other devices select add network printer.