After about a week of in-depth research, I started to flip my AP Govt class this past week. I'm now posting videos (screencasts) of content that I would usually deliver at the front of the classroom and having students watch and respond to the videos before they come to class. Once in class, we can go over any confusion students may have encountered when watching the videos, then delve deeper into the topic or apply the topic to new situations.
I'll have more on my progress in the coming weeks, but the equipment/software I'm using are
Screencast-o-matic (hat tip to Ken), an external camera/mic by Logitech ($40), and Google Forms.