Go to Godaddy.com, or the registrar of your choice, and check to see if the domain you want is available!  There's a search function right on their homepage.  Follow the directions to sign up, and you're ready to roll! 

If you're going to use my design services, please make SURE the registrar you use has full DNS control, ask them if you're not sure!

For any business sites I'd strongly recommend buying the .com, .net, and .info version of your chosen domain (if they're available).  You can point them all to the same site, but it makes you easier to find, and your competition less likely to get in the way.