Multiplayer games over networking are mostly very complicated. It's never built for beginners: it will be build for experienced programmers which really want to sell their game. The easiest framework for multiplayer games over the Internet or over Bluetooth I know of is GameKit in iOS, but that's not really for beginners, it's also not using java.
Well, probably you have to change some greenfoot code and search the web for possibilities to do it in raw java. So that would be even a challenge for most of the people here!
There are only two scenarios that I know of that have been created thus far that deal with any type of user interaction. One is Multi-chat by DonaldDuck; the other is Private Messaging by yours truly. The interaction between users in both are nothing near what one would need for most games (except for maybe chess, or other slow paced games as such). What kind of multi-player game are/were you intending to create? What kind of response time-frame are you looking at (between moves)?