In order to network, you need to install a NIC, or network interface card, inside your laptop.
Most laptops sold today come with a NIC standard. You can tell that it's there by looking for the RJ-45 hole or thing on the sides or back of your laptop's case. If you see that hole, your laptop is ready for networking. You just need to use a network cable to connect your laptop to the network jack in the wall, to another PC, or directly to a network hub, switch, or router.
If your laptop lacks a NIC or the RJ-45 hole, you can add one easily, by using either a PC Card or using a USB-Ethernet adapter.
The cable you use to plug your laptop into the network is commonly called Ethernet cable. It's also known as CAT-5. You can buy it in assorted lengths, colors, and flavors. It's available at any computer- or office-supply store.
RJ-45 holes look like phone jack holes, but they're slightly larger. Do not confuse them! If the Ethernet cable doesn't fit into the hole, that particular hole is a phone or modem jack, not an RJ-45.
A hub, switch, or router is a hardware device designed as a central locus for all computers on the network. Everything plugs into the hub, switch, or router.
A hub is simply a place where Ethernet cables from various computers (or printers or modems) plug in.
A switch is a faster version of a hub.
A router is a faster, smarter version of a switch.
No, you don't really need a hub-switch-router thing. If you're just connecting two computers, plug an Ethernet, or CAT-5, cable into each computer's NIC and then you can do what's called peer-to-peer networking. This is the fastest, most efficient way to connect two computers for exchanging information.