DUMB QUESTION?

[Sharon]

I must admit im a newbie here! But I do have a question that it seems
the people here have the knowledge to answer so here goes!

 I am looking to run a service that will allow people to have their name
run off of one domain "theirsite.mydomain.com" "theirsite2.mydomain.com"
and on and on! The problem im having is i can't get the name server to
send the surfer to the right directory. Every time a subdomain is typed
it sends them to the main domain. Is there a way to send the surfer to
the proper directory thru DNS or do i need something else?
 I have seen this done many times before so i kone it can be done, I
just don't know how! ANY help would be most gratefull!