I've had some success, I just wanted to share it with any lurkers out there.
This tutorial: Building an Internet chat system - JavaWorld
It involves ServerSockets, I compiled/ran the client on one comp, and the server on the other one, and I'm able to connect, by providing the name of the host computer on the network (they're connected to the same router). To see if I could theoretically do this remotely, I set up the router to use a "virtual server", so that anything entering on a certain port would be re-routed to the host computer (whose server app uses that port). I had the client use the ip address of the router (google: "my ip") and the same port.
I've yet to test this on an actually remote system. Not the most user-friendly solution, either, but its a start! (I think)