First off, what the heck is computer networking? 
Computer Networking is nothing more than a collection of computers connected to one another via cabling and network equipment such as modems, routers, and switches. Modems, routers, and switches are nothing more than electrical equipment that controls the actual traffic on the network. And what is the traffic, it is your emails, printer requests, chats, applications, and anything else you do on a computer that requires the use of one or more systems beyond just your PC.
Networks exist not only to allow inter-communication between network participants, but to share resources such as printers and file storage. Also though, networking also allows for a single access point to the Internet (such as a DSL, Cable, or commercial Internet access line that is ran to your home or office) can be shared by many PCs by using network equipment to 'splinter' off access to 20, 50, or 70 computers off of that single access point which is installed by your phone company or cable provider. This is a huge benefit to home and small office needs.
It's certainly not uncommon anymore for a residence to have more than one computer and usually there is only one connection to the Internet. The connection can either be shared by everyone, or can be 'split' using compuer networking equipment so everyone can access the Internet at the same time! If your connection is either a DSL or High Speed Cable, you can purchase a Home Gateway (not very expensive - between $50 and $200 depending on what you need and get which we'll discuss later). A Home Gateway tends to be called a home router as such, but it is more like a switch and your DSL or Cable modem is more like a router. But all that matters is that you know what to buy and how to hook it up to expand your Internet connection to multiple computers!
Now your DSL or Cable provider will want to sell you a Home Networking Package which is nothing more than them installing the home gateway for you and charging you double a month for the connection. Save your money and learn a few simple steps that you need to in order to take care of this project on your own. Self Reliance is great!
Once you've made the decision to setup your own home network, now comes the decision using cables or go wireless. 
Using wires (ethernet cables that make a physical connection between the home gateway and your PC or notebook) is easier and a little quicker, but at the expense of having unsightly cabling strewn through your room(s) that you will always trip over for some reason. Wireless home networking is the way to go and not as difficult to setup as you may think. Either option will work and save you money from paying for a 'home network package' from your provider.