In general there are several components you need to create a home or small office network:

Computers: You need two or more computers for a network.

Network adapter: Often called a network interface card. Network adapters connect your computers to the network and allow your computers to talk to each other. Network adapters can be connected to the USB port on your computer or installed inside your computer in an available PCI expansion slot.

Network hubs and cables: A hub connects multiple computers at a central location. A hub is typically used when connecting two or more computers to an Ethernet network. A hub is not required if you are going to connect your computers through your phone lines using a home phoneline network adapter (HPNA) or if you use a wireless adapter. Using Ethernet or HPNA, you need cables to connect to either a hub or the phone lines. You can also use IEEE 1394 network adapters.

Modem: This includes 28.8 or 56 kilobits per second (Kbps) modems, wireless modems, Integrated Services Digital Network (ISDN), Digital Subscriber Line (DSL), and cable modems

Source: microsoft.com

More information about different topologies you can find here:

Bus Topology
Star Topology
Ring Topology
Mesh Topology