What kind of working example are you looking for?
The page I link to in the WP Codex http://codex.wordpress.org/AJAX_in_Plugins give a pretty in-depth explanation of using AJAX in WP. The only real difference is that instead of using JQuery for the requests you use the scripts in this plugin. I think my documentation pretty well covers calling my script to make a requests.
I do plan at some point to put a basic tutorial together, but that requires time to kill which is something that is currently in short supply.
If you have specific questions on how to do something I will do my best to answer them.
Currently the best working example of this plugin being used is in one of my other plugins which can be found here: http://parasrch.jayaitch.com/
Since I have not heard back on this I’m going to go ahead and close this topic. If you have specific questions I can help you with just open a new one.
Well your working example needs a login.
Sorry, I took done that plugin and the site. The parametric search plugin was too bugging and I didn’t want people using it until I could work some major kinks out of it. The documentation here is complete. If anyone has specific questions about the documentation or how to do something specific I can try to answer questions. The focus of this plugins is other developers.