First of all you need to find a domain name registrar, preferably not the same company that you plan to host your website with. There are TONS of domain name registrars so you should have no problem finding one, but don't pay more than $17 per year for a new domain name.

Example of part of the form:

Registrant: Your name
Address: Your Address
Administrative Contact: Usually you don't fill this out.
Technical Contact: Sometimes you need to fill this out.
Name Servers: You should be able to change the stuff here whenever you switch web hosting providers. Your host will, or at least it should, provide you with the information that you need. If you don't have a host yet, don't panic most registars will register the domain then put a "www.your-domain.tld coming soon" sign.

Note: They might require you to fill out a couple other things too.

A TLD is a Top Level Domain name. This site is used to be at www.build-a-website.cnwcentral.com. CNW Central.com was the top level domain and this website was a 2nd level domain, or sub-domain because its at *.my domain name.com. I own www.cnwcentral.com just to let you know. I couldn't buy www.build-a-website.com/.org/.net/.info because some people decided they wanted to use them as doorway pages. Luckly, one of those people let the .net version of the domain name expire and I registered it.

There are about 5-10 domain name extensions that you can register but I'll only cover the most important ones. Go to http://www.icann.org/tlds/ for more information.

.com Dot com's have turned into all purpose domain names. My former school librarian told us that .com's are only used by companies, that's not completely true anymore. Lots of information sites and sites about random subjects use .com's.

.net Dot net domains were originally intended for network providers, but they are currently all purpose domain names.

.org Dot org are mainly used for organizations. They were created for organizations that didn't fit in with other TLD's.

Domain name parking is when you register a domain name but you don't have a website yet. If someone happens to find your domain a page will show up that says it's been reserved/parked.

The WhoIs database contains information about who registered a domain and when it was registered. It can take a around a day for changes to show up in the database. There are many websites that allow you to search the WhoIs database. Also most nations have a their own version of the WhoIs database.

I personally use WhoIs.sc if I ever need to WhoIs someone's domain name.