What's the brand/model of the printer?
If the printer has an ethernet port, then just plug it into the router. There should some sort of configuration option in the printer to then print out or show you what the router gave it as far as an IP address. Once you have the IP, you can add it to any computer on the network from the devices and printers menu.
Before you connect to it though, I would load the drivers for the printer on whatever computer you want to connect to beforehand.
This. Look in the manual to see how to setup the printer to have a static IP address on your network, and then map the printer via that IP through the Add Printer wizard.
Choose "Local" and then create a new TCP/IP port, and type in the local IP address of your printer that you set. It should connect and either prompt you for a driver (download from their website) or Windows Updates should take care of it.
Just looked and it doesn't even have a USB port.
Yes it does. I looked it up.
Brother International - - MFC-7360NFlexible connectivity. A built-in Ethernet network interface allows for sharing with multiple users on your network or connect locally to a single computer via its Hi-Speed USB 2.0 interface.