How does a (non-pilot) arrange a tour of an ATC facility? Although the question has been asked for pilots, how does a civilian get access to a ATC facility? I regularly listen to Live ATC, and I'm incredibly curious as to what the inner-workings of a tower look like. 

Even at that, is there a live video feed of ATCs?
For tours, call the facility and say you're interested in aviation, and would like a tour, same as pilots. Depending on the facility, business hour tours are preferred, though others will let you come any time they have available staffing to escort you around.

As far as I know, there are no video feed of any ATC facilities.