After choosing the domain name, register it from domain register service providers like http://www.godaddy.com, The name what we chose for a site could be already existing. Which means the name is being used by someone else. In this case, go to any of the domain registering sites and get the details of the domain name owner. Then check with the website owner whether he is willing to sell the domain name. If not go for another name. Most of the people reserve domain names to resale them.

If you desperately need a particular name, which is not available, follow the suggestions given by the domain registration service.