Or post a URL to your site on slashdot... that'll bring the "free unlimited bandwidth" hosts to their knees (usually).
A domain name is basically an entry in a table that translates "easy to remember names" into "hard to remember numbers". The "registration of a domain name" is nothing more than the creation of this entry (and the related ownership details etc in an admin database).
Many companies offer this registration service - and as posted, you should not be paying much more than $10 or so per year for this process (although different domains will cost you different amounts: .tv costs more than .com).
Once you have a domain registered, you can often update the table entry using a web admin control panel. This gives you the ability to utilise almost any web hosting company to physically store your web site. Your web hosting is entirely seperate from the domain hosting.
Some companies offer both services... and some of them have various bundled packages where they grant free domain registration with certain restrictive conditions. I would consider these bundled packages only after reading all the Terms and Conditions very very closely. If it sounds too good to be true... it will be.
I have used
to register domains in the UK, and then used their web control panel to change which website the domain "pointed to". Of course, I also used
to both register a domain as well as host the corresponding web site. Usually you get a more "integrated" suite of solutions if you go for a solution like the latter.
Sorry for the lengthy rant... hope it's of value to you.
Jeff