A critical piece of hardware is the network adapter. Some computers come with the NIC and accompanying software drivers pre-installed. If your machines do not have cards built in, that's a separate purchase and installation for you. Whichever NIC you choose, you should try to settle on the same brand for all your computers for easier troubleshooting.
All networks also require the use of a hub.
A hub essentially acts as a central traffic cop for the network. The hub manages receiving and transmitting data from networked devices. Each computer and peripheral that you want on the network must have a cable that runs from the NIC that is installed inside it to the hub. Hubs vary in price, depending on the connection speed they support and how many devices they can connect. Hubs come in many different port configurations.