A domain name registrar is a company accredited by the Internet Corporation for Assigned Names and Numbers (ICANN) and/or by a national ccTLD authority to register Internet domain names. Thus, make sure you register with an ICANN Accredited Registrar, and register in your own name and email address. Although you have a webmaster who act on your behalf to register a name for you, be sure they register it in your name, not theirs.
Domain registrars offer a tool to check to see if the name you want is available. If a domain is available, you can buy it. If someone owns the domain, you can contact the current domain owner, and contact them to buy their domain. Many domain owners are willing to sell their domains, usually with higher prices. Good domain names sometimes sell thousands of dollar.
