You register a domain with a domain registrar or one of their agents. Typically, a domain name will cost you $35 for 2 years - less depending on the top level domain in which you register i.e. .com .net .com.au .net.au etc.
To get a domain registered will require that someone will manage the DNS entries on yuor behalf, assuming you're not in a postion to do this yourself.
Most hosting companies will do this for you when you take up one of their hosting packages, most will also manage the DNS entries required for your domain name. As someone stated previously, this is often referred to as parking a domain. i.e. the domain name can be looked up but it has no content to look at.
For example, I have a domain name registered with
Webcity, they act as an agent for a domain registrar Enetica. The domain name cost me $35 for two years, Webcity charge me $6.95 per year to manage the domain name system entries. I also have hosting through them but that is a seperate agreement over and above the domain name side of things. Basically, the $6.95 charge, is to make sure that the DNS entry for my domain name points to the IP address of their server that has my website on it.