It's so hard to boil things down to the basics so that they can be explained easily. Hopefully this works toward that purpose. It will be presented as part of a larger document, addressed in-character to player characters who require a basic understanding of how the tech works.
A portion of the fluff text is below, then the primer. Forgive it, as it's rough, but I thought you might enjoy the work in progress; click the image to view a larger version in another window.
Understanding our world as it exists today is a study of equal parts history and science. History, to understand our forebears and the society that they built, and science to understand the complex technologies that led to their sudden and complete downfall. Due to the incomplete nature of our understanding on both those points, a full discussion on these topics is highly involved, often delving into theory and the best guesses of our scholars. For our purposes today, however, we can go over what we understand of the history and technology of our world from just before The Collapse until now, using as little conjecture as possible. For your purposes, this should suffice.