Firstly, you need a high-speed Internet connection. 512kbps is the minimum. However, most broadband connections (I think) are limited to 256kbps downstream -- which is what will happen if you have your PC hosting web documents.
Secondly, you need to decide upon the server software you wish to use. I advise against Microsoft IIS because it is big, clumsy and full of security holes. Apache is probably the best solution since it runs on something like 75% of the world's web servers. However, it can be difficult to configure. Probably one of the simplest but functional servers is Abyss Web Server. But whichever option you choose, think about whether you just want to server static HTML pages or whether you want some sort of server-side scripting or database. If it was upto me, I would choose to run Abyss Web Server with PHP and MySQL (databasing). You can test out whether the software works by typing http://localhost/ or http://127.0.0.1/ in your web browser. Then go to What Is My IP? and copy and paste the number into the address bar with a preceding http://. For example: http://123.45.67.88. You might want to phone up a friend and ask them to type this into their web browser to see if it works. If it does work it means your ISP isn't blocking port 80 and you have nothing to worry about. If it doesn't work, it means you have to run the web server on a different port. A good second port is 8080 but you could choose any.
Then, you'll need to establish whether you have a dynamic IP or a static one. For a static one, you simply register a domain and use a service like zoneedit.com who provide a free DNS service. In case you didn't know, DNS is what every web browser uses to turn, say, www.google.com in its IP address, 66.102.9.99. This is all described quite clearly on their website.
Once your domain points to your IP address (which may take a few days to propogate throughout the DNS servers) you have a working server! The only thing is: if you want people to be able to visit your site, you have to keep your machine on 24 hours a day, 7 days a week.
If all goes to plan, you should be able to save web files into your web server's root folder and then access them by typing www.yourdomain.com/yourfile.html. If you want any more information (and I bet you will), the best website is probably dslwebserver.com.
I hope this helps,
James