Serious about building a website? The first thing you need to do is purchase a domain (assuming of course that you've already established a name for your company). Registering a domain is more or less pain free and depending on what type of domain (.com, .org, etc.) not too hard on your wallet either.
The easiest way to register a domain is through one of any number of websites like godaddy.com or register.com (the first two hits on a Google search). Domain registry sites allow you to check the availability of a domain name, and then to purchase it for use.
Once the domain is purchased, it needs to be mapped to wherever you are hosting the actual content of your website. This is accomplished by inputting the proper url into the DNS servers with whatever registry site you've used.
For example, if you use a free blogging service like Blogger or Wordpress, you would look on their website for instructions on how to map your custom domain. They would provide you with the names to input into the registry site, and then you would insert the names on the registry site through your account options. The exact process will differ based on your host and on your registry service, however, the basic steps of finding the name server information and then inputting that information into the registry site are the same.
While some of the terminology may make the process sound intimidating, this video
will show you how to register a domain name using godaddy.com. (Please note that the video will walk you through how to purchase a domain NOT map the domain--for domain mapping help please read here