First step is to set up DNS (Domain Name Service). You'll need one or two such servers which are responsilbe for turning names in your domain (like www.yourdomain.com or mail.yourdomain.com) into IP addresses.
Normally DNS comes with hosting accounts (e.g. when you rent a server and space from folks like bluehost.com or dreamhost.com) they will tell you the IPs of their DNS and they will do the IP resolution for you.
Otherwise you either have to have a DNS installed on your computer (not a good idea unless it's up 24/7) or just order DNS service from a place like dyndns.com. There you'd enter the IP of your home machine as the IP for let's say www.yourdomain.com and then http://www.yourdomain.com/ would end up on your machine.