Can a printer be connected directly to a router?

I have a HP 7210 All-in-one printer that I can use from my computer with the USB cord. I use a wireless router for my Internet access. I can plug my printer directly into my router using the CAT5 cable but I can't seem to find out what settings I use to access the printer through the router. I know it must be something easy that I am missing here. Do I have to have the printer connected to a computer on the network to access it through the network from another computer?

You say you can plug the printer directly to the router with a CAT5 cable. Was this a question or a statement? If a statement then you should be able to check the IP address the printer is using through the router and then setup a network printer in Windows, pointing to that ip address. If it was a question, then you would need to see if there was a CAT5 connection on the printer. If not, you can buy print servers that are little devices that have USB on one side and CAT5 on the other, so the printer plugs into the USB and the router plugs into the CAT5.