It is very easy to buy domain names. There are several domain name registrars that offer domain name registration for just a small fee. You can register the domain name for a few dollars or even less. After you have registered the domain name,then you can simply type in the keyword and click on the search box on the top-right corner of your browser. This will bring you a list of the many domains available.
After you have searched for one you like and clicked on the search box,the domain registrar should come up and show you the details of the domain. You should be able to see the domain name,its extension,how long it has been in existence and what other people have called it. You will also find out who owns the domain. You will find that some domain registrars only offer registration for free,but there are others that will charge you a nominal fee for this service.
You should decide the amount you are willing to pay for your domain name before you go to register it. If you do not want to be forced into paying a large fee,then consider using an online domain name broker service for your domain name needs. These services will search for domains for you and will also provide you with suggestions as to the best domain name to buy.