Domain Names are associated with a server number. To find out the availability of a domain name of your choice, go to: http://www.networksolutions.com/
http://www.icann.org (because it shows lists of places to register names)
Once you find a domain name is available, take it immediately.
You first need to reserve that name, then, as a separate action, you need to “park” that name on a server. You do that by renting space on a server to store your webpages.