You don't have anything in your main. You have to put an infinite loop in there.
Also, if you are doing this you then need to invoke the object since the ServerSocket is a part of the class members and not a part of the main. At least I think so, let me double check.
Yep, you need to invoke it then. You also need to override the constructor to add a checked exception for the IOException since it won't handle it otherwise.