One of the first things you'll want to do when building a new website is to pick a URL for your site - also known as a domain name. Here's how you can check if your domain name is available.
Visit http://hostmonster.com and click "Domain Check".
Checking a domain name is completely free, and you can check as many domains as you want. It'll ask you to choose a hosting package, but it won't charge you unless you want to buy the domain after finding it (also optional, but very convenient if you want to reserve the name right away).
Once you're on the domain check page, enter your desired URL and Hostmonster will check if it's available.
One thing I love about this free domain check service is that it offers a long list of alternative domain names if the one you're looking for is not available. I find that very useful when trying to come up with ideas, and they also give you a list of other domain suffixes, like .net, .org, .us, etc.
Happy domain name hunting! It's kind of a land grab out there and you may find you need to get pretty creative to find just the right name for your new site.