You can use your own computer to host a webpage by seting up a web server like apache and a database like MySQL. There is a package that includes everything you need to do this called XAMMP.

Once you get it setup the way you want it, since most people use dynamic IP's, you can set up a dynamic DNS to have a static link to your site. Once you have the static link, just buy a domain name for like $8 a year and forward to your dyndns link.

You can set up a dynamic dns at http://www.dyndns.org

This method is ALOT cheaper than paying some third party to host your site. And if your site ever goes down, you can only blame yourself. Also, the space you have is limited by your HD. You can have as much as you want.