1. Pull 5-6 screen shots of various sections of the process, making sure that at least one of them shows assembling the puzzle, then print, insert into a simple frame, and post in various but prominent places around your booth. Another option may be to align them side to side, from start to finish, in your highest visibility yet out of the way area.
2. Edit the video to no more than 3 minutes, showing aspects of the cut, with the last 10-20 seconds of final assembly. Someone interested in seeing the process likely won't stand around for 24 minutes to see the end result, but they will stick around for a few minutes. Loop this video so that you can stay focused on visitors.
3. Whether you reshoot the video or edit this one, use sections without your hands in the way. Ensure that the video is focused on the puzzle cutting process.
4. Consider adding music to the video. Don't try speaking and describing the process, as this would be lost in the noise of the fair/event/show. Music will gain attention without needing to be clearly heard.
These are the things that I would do to gain the most marketing mileage from your efforts.