Does anyone know how I can begin hosting other peoples web sites on my server

On your server at home? Don't even try it. Your connection is way to slow to be serving other peoples websites. You can get a reseller account with a major hosting company, that would work much better.

what exactly is a reseller and how does it work?

Basicly, a reseller account is nothing more then a shared hosting account with a hosting company.
You get a big chunk of space and bandwidth and on the hosting company's servers and you have the ability to split that space up into your own packages and offer them for sale. You can host multiple domains, add remove features for your clients and add/remove accounts on your own.
Usualy, your clients will not even know about the company your using as they will come to you for support, upgrades or whatever else they need. The hosting company you resell for will, for the most part, be invisible. What they will do, however is manage the servers and upgrade software as needed to keep the server secure. All you need to do is worry about getting clients and setting them up.

There are many, many hosting companies that offer reseller accounts. One of the bigger ones is http://www.hostgator.com/

You could also get a shared hosting reseller account from here http://www.aplus.net/hostingresellerprograms.html

I would suggest you look around for reviews on the above 2 suggested host. Just so you are aware of others issues with these current companies and make an informed decision when you do decied to choose a host.