To host your own website you will need the following;
1. Good broadband speed connection at home (ISP)
2. You will need a static IP (you can get this from your provider for a fee) or a dynamic IP DNS service such as
DynDNS: DNS Hosting, Email Delivery and Other Services .
3. You will need to by a domain name for a reputable domain name register and get some software to be able to create/edit a website with (or use a free website builder program from whoever you purchase your domain name from, if they offer such service).
4. You will also need to setup a server at home using Windows (IIS) or Linux (Apache), you can run a server off of a Windows XP Professional machine by installing IIS on it.
5. You will need to know how to configure your home networking equipment to have a static IP or use the DYNDNS service and need to know how to configure your server to host your website on.
I have only briefly listed some things you would need to acquire before being able to host your own website at home. I have not mentioned the cost of hardware you would need either, just wanting to let you know it takes a lot more then some people think to be able to host your own website at home. If you still want to do this then let us know and we can take you step by step.
Side Note: This is not to be taken on by a novice computer user, a person needs to understand the implications of what they are doing when they want to point people form the Internet to their home network...security, security, security.