I found the networking tutorials on the java website to be very valuable in making this chess game. it's probably not the most efficient networking, and it was only a little project to play around with, but i hope this helps a bit...
I did play it on the internet with a friend once, it worked quite well, until we both tried to move a piece at the same time. you can run it twice on one computer and just host with one instance and connect with the other
this JAR is executable, but my ISP or internet explorer (one of the two) seems to want to download it as a .zip. just rename it to .jar and you should be able to double click it to run.
the source code is inside. you can unzip it.http://www.adam.com.au/kellyjones/javagaming/JMChess.jar