If you are interested in setting up a simple website similar to this one, read on.
Consider Weebly, the service I am using here which provides the easiest drag-and-drop interface you can imagine--no programming experience necessary. Other popular options to consider include Posterous, which might be better for sites that only have a blog since you just email them your content, or Blogger. Since I wanted to have a homepage in addition to a blog, I like seeing the layout before it gets published, and I enjoy the flexibility of being one-click away from adding additional blogs to my homepage, I chose Weebly.
If you would like to customize your web address with a domain that does not include the "weebly" or "posterous" that is included by default, you could test domain availability on domai.nr which is particularly helpful for finding creative domains you would not have otherwise thought of. This is a better approach than simply Googling your potential domain or entering it into your address bar for the reasons listed here.
Once you have found a domain you think could be worthwhile you will need to secure it at a registrar with a credit card. While GoDaddy has marketed its way to being among the most well-known registrars out there, I have had phenomenal customer service from 1&1 and recommend using them instead since their recurring prices tend to be a bit lower as well and the offer different introductory promotions every month.
Assuming you use Weebly, you can follow the simple instructions listed on Weebly's site to point your web address visitors to your future site, regardless of who you used to register your domain. Other build-your-own website services such as Posterous generally provide similar instructions in their FAQ.