There are several types of printer networking you can use: either sharing a USB printer that’s hooked up to one Mac, or setting up an ethernet printer directly on the network for all users, or using a wireless printer.
The difference is in the printer itself: does your printer have an ethernet port (which looks like an oversized telephone jack) or is it wireless-capable? Or does it only have a USB port? If you are shopping for a network-capable printer, these are the same details to take into account.
If the printer is not wireless and doesn’t have an ethernet port, then it will need to be plugged into one Mac via USB and shared by that Mac. That means that one Mac will need to be on all the time so other network users can access it, even though the rest of the network is ethernet. This kind of network connection is really just printer sharing and is very limited and probably not what you want.
If the printer has an ethernet port, it can be plugged into the network directly – at the router or hub, where all the other network cables are plugged in – and can be set up to be used by all Macs (and usually Windows PCs, too) anytime, and no one particular Mac or PC needs to be on. This is real printer networking, and you will need to get a printer with an ethernet port and set it up on the network.
Wireless printing depends on the printer, too. If it is fully wireless capable, it will have its own wi-fi built in, so any PC or Mac can use it without having to go through the rest of the network, if there is a network. Some wi-fi printers don’t need any other part of an existing network – either wireless or ethernet – to work for all users.