You have to pay for one. Usually if you sign up for a web hosting service (a good one), they'll give you the option to choose your domain name during the sign up, and then you'll have to pay for it periodically.
Alternatively, you could use a free web hosting service. Your domain name would include the username you choose during the sign up, and also part of the website's name.
www.150m.com is the web hosting service I'm using right now. It's free. Paid for ones are much better though if you get a good one. In 150m's case, it will be like this:
username.150m.com
Some free services have more annoying names, like www.freewebs.com/username
DO NOT use any of the paid for services from the free sites. They're not worth it. There are better deals out there.
I'd also like to note that this doesn't really have a lot to do with Flash, but I guess if you don't know what you're doing it would seem that way. And would someone please post some replies to the topic mentioned in my signature? I'd appreciate that.