Jim... I'm also an engineer (Chemical) that migrating into web development about 5 years ago. Ironically, I'm also just starting to use AJAX in some of my projects. Fundamentally, there isn't much too it. Just using javascript to pass info back and forth between server-side script without form submissions/page refresh.
It can get fancy, like the scriptaculous drag-and-drop shopping cart, but I've been using it for more practical purposes like real-time form validation against a database.
Check out these leads...
http://script.aculo.us/ (<- sophisticated effects)
http://ajaxagent.org (<-very simple/powerful PHP/AJAX js class)
P.S. in editing this post, I've found that this forum uses AJAX to allow the author to edit their post in-line without page refreshes. Look in the source for the call to ajax_prep_for_edit