All of the authorized domain name registrars allow the public to conduct free domain name searches. In most cases, all you have to do is enter the domain name you want into a form on the registrar's Web page — if the name is taken, the form will list the current owner's name and contact information. (If this is the case, be sure to read How to Buy a Domain Name Owned by Someone Else.) If the name is still available, you can fill out another online form to register the name yourself.
Other Web sites, including many Internet service providers and Web hosting services, also provide links to this domain name database. You should never pay just to search for a domain name; most reputable sites will provide this service for free, and the ones that don't might be trying to exploit inexperienced Internet users. If you want to reserve an available domain name, however, you'll need to pay the registration fee.
Before you register your domain name, you might also want to check with the U.S. Trademark Office to make sure someone isn't using the name as a real-world trademark. Registering a domain name won't automatically protect you if someone already holding a trademark on that name decides to take legal action. If you have any doubts about your right to use a domain name or about how to protect your domain name from illegal use, check with an attorney — your business name is too important to take any chances with it. Read Where Can I Find a Business Lawyer? for some good advice.