Well, if you want it free, don't expect someone to help you out to make it professional or good. You have to do it yourself. It can be easily done by HTML and PHP if you want the basic stuff. You can also get into more advanced stuff with PHP like profiles, user registrations, forum, chats and something like that but that takes a little more than basic knowledge, but making the basic isn't that hard.
Plus, there are also source codes on the internet of flash game websites.
If you mean free design then you could do it yourself or have some one do it for you. If you talking a server then you probably have to register it with a company such as go daddy (bad example but a well known one). They are usually cheap though. Armorgames uses ThePlanet which merged with SoftLayer and all services they supply are now under the SoftLayer name. Hope this helped.
