How should I go about getting a website domain from someone who already has it?
The best way to do this is to see to whom the domain name is registered. You can do this via a WHOIS look up. This web site will help you:
This will, most often, give you the contact information of the person owning the domain name.
Contact them and ask if they are willing to sell the domain. Sometimes the website itself will list the owner's information. Come to an agreement on a fair price for the domain and be sure to use a service like Escrow.com to arrange the transfer of the domain to protect both your and the sellers interests.