This is a very simple Chat Room applet. Note that if you try to load it from your local machine as opposed to a server, you won't have much luck, since Java Applets are only allowed - for very good security reasons - to open a network connection back to where they came from! Load it from the server instead.
The Chat Room should appear in its own window. If it does not, check to make sure that you have a Java-enabled Web Browser. Check to make sure that the Chat Window is not hidden behind another window, too (on systems with an IconPanel or a TaskBar, look there!).
Use The Source, Luke. Alternately, see the server source. Also see shared Chat class source.