The simplest process i came across while searching for a way to host my own website on my own server without getting in hassles of choosing web hosting service was www.no-ip.com
All you have to do is register for the free service there and you will get an email with the steps to follow with a client software which you have to install on your machine. After that you will have to configure your ADSL Router ( if you are using it to access internet ) to forward port number 80 to the ip address of your machine which is going to be a web server . And you are done now the client software you installed will automatically update the IP in DNS server of no-ip.com and you can access your site with
<your site name >.no-ip.org
this kind of domain is given when you use free package and there is also an option to pay and use your own domain but i haven't checked that yet . So enjoy and Host your site with a dynamic IP !