It's pretty simple actually...
Register the domain name, and point it to the static IP address that your server is on... set everything up on your network so that all inbound requests go to that local IP and you should be pretty much set... you of course need hosting software (IIS, Apache, etc) and some other stuff... but the general idea behind it isnt that complicated when you look at it...
Static IP is required though... or if you are on DSL or somethnig you can always get a static ip at like
www.no-ip.com or something... otherwise you would need to change your DNS settings every time you got disconnected.