The most basic of networks will require you to be connected to the internet normally! This is done via device called a network router or gateway and it opens the door from your local network to the wider world of the WWW!
Depending on the size of the network you may have a separate switch but your router will probably have 4-5 switch ports built into it - It'll also likely have a Wifi Access Point built into it too - both of which might be swapped out for separate boxes as things get bigger and more complex.
Basically though whether by a wire or by a cable your computer has a special port on the back which let's it talk to the router and so other devices plugged into the switch on the router be that another computer or a printer.
Each device on the network has an address - normally called an IP address which will normally be something like 192.168.1.2 and so on. And each machine will know the routers IP address to go to the internet.
DNS is the only other part of the puzzle here. All those numbers aren't human friendly BUT they are very computer friendly so DNS is the middleman between these two camps. Hence bbc.co.uk (easy for you) via DNS is 151.101.64.81 - easy for the computer!