When someone types in a domain name like http://www.mydomain.com, their Internet service contacts InterNIC, the organization responsible for keeping track of domain names, and gets the appropriate IP. This is how your computer actually contacts the remote computer.
So, before you can use your domain, you have to register it with InterNIC (any domain registration service will work). At this point, you can tell InterNIC what your IP address is (you should be able to manage this through the company you used to register your page) and when people type in your domain, they will be pointed at your web page.
Note: you have to have a static IP address for this to work.