From the Albuquerque Journal a picture of the system used by the "Starfire geeks":
and a close-up from AP:
They used a Questar 3.5" telescope on a fixed tripod and the tracking
mirror (which is a flat mirror and a high-precision pointing stage) to
point. They started putting things together the evening before, just
on a lark.
"They mounted [the Questar] in front of a set of larger movable
satellite-tracking mirrors that had been salvaged from White Sands
Missile Range two decades ago.
"Old but still reliable, the mirrors tracked the shuttle, reflecting
its image back to an instrument room where the telescope was mounted."
...emerged from clouds...to clouds...24 seconds...only time to snap one
picture...36 degrees above the western horizon, nearly 70 miles away at
the time.
Not quite sure to understand what we are looking at.
The camera or whatever was attached to the scope is definitely not consumer
grade , no camcorder or webcam . There are other gizmos in the image which
look professional. Does anyone know any of these pieces of equipment?
Edited to remove that huge picture that ruins all the formatting of the thread. If you want to use a picture that is larger than the normal screen size the just post a link to the page with the picture instead of the picture itself! 
Sorry about that - won't happen again !