If upon verifying a domain vacancy you find out that it has already been taken, it means that someone else is the domain holder. Actually this person is not the domain owner. The person has only rented the domain from the owner for a limited period of time and can run their site on it.
To find out whom the domain belongs to, you can do so through www.whois.com, where after entering the domain you can search for the information to whom the domain is registered, the domain status, from when the domain is registered and the domain expiration time.