How do I discover peers and send messages in JXTA-JXSE 2.6?

Question

Using JXTA 2.6 from http://jxse.kenai.com/ I want to create application that can run multiple peers on one or more hosts. The peers should be able to find each other in a group and send direct messages as well as propagate messages.

What would a simple hello world type of application look like that meet these requirements?

I created this question with the intention of supplying a tutorial like answer, an answer I tried very hard to find two months ago when starting to look at JXTA for a uni project. Feel free to add your own answers or improve on mine. I will wait a few days and accept the best one.