If you connect the printer using USB to the hard wired pc, and you have clinet for microsoft windows and file and printer sharing enabled, this is the easiest way to set up the printer. Set it up on usb, and in the start -> settings->control Panel -> printers and faxes right click the newly installed printer and selec the sharing tab. Enable sharing with share this printer.
Then remote pcs can browse the pc and will see the printer share.
easiest way to browse, open a dos window and type start \\IP_OF_PC_WITH_PRINTER\
It should pop open and you can select the printer, right click it and select install printer. You will probably need a printer driver.
Use of this printer will require that the PC be on whenever you want to print, and enabling printer sharing has some security aspects.
If you put it on the usb of the router, it is a bit trickier. On the clients you will need to open the printers and faxes window, right click the root of the folder, that is not on the printers, and select add printer.
When you are in the add printer wizard select local printer ( I know, it is not really local) and select NEW PORT. Select standard tcp port, put in the ip address of the router, and select ok. Then you will need to select the printer model and find the drivers....
So its up to you.