Here's a quick visual rundown on how to register a free domain with BlueHost when you sign up for hosting.   Not only can you get a free domain with hosting, the setup fee will be waived too.  Be careful with other web hosting providers sometimes they hide a pricey setup fee and slap it on you when you least expect it!  (Think airline tickets!)

By the way, the process of signing up for a hosting package + domain is (hopefully) very similar with different providers.  I've chosen BlueHost here because they are the most recognized name in web hosting and have been superb in my many years of using them.  So as a part of my appreciation, I'll use them as an example.  Thanks BlueHost!

Follow the big Sign Up sign! 

Almost always there will be a big sign with overly happy people behind it (yay!).   This is a view of BlueHost's homepage.  

While you're here, take note of a few things.  In the upper left is where you will sign in after you have an account.  In the lower left is a button to start a live chat session where you can ask any type of question to a service or sales representative -- which I might add is very quick and responsive.  

After you click "Sign Up Now..."  you'll come to this screen which asks you what domain name you want to register.

 Enter yor domain name as a new client and click next.  BlueHost will then check whether or not your domain is available to reserve.  If it is already reserved, you'll be greeted with a screen like this:

You might have to tweak your domain name a little bit.  Perhaps you could separate words with hypens like, ah hem, easy-website-design.com.  Ultimately when you decide on a domain name that isn't taken you will be greeted with the wonderful message of Congratulations!

On the same screen you can then proceed to fill in all the run-of-the-mill information, which includes your business name (which can be your domain name), address, contact information, and of course payment method.  You can even pay via paypal if you prefer.

Also, I recommend you "Add BlueHost Domain Privacy" which is free.  This will prevent spammers from sending you unwanted email and snail mail.  

The rest is history!   It's just like checking out at any other online store!

Where to go from here:

Hey what are you still doing here?  Well now you can move on to install the Joomla content management system.  And if you ended up using BlueHost   you can do so using Fantastico!