Nice suggestions, Dick. I also am a teacher, so I enjoy teaching casting, a nice break from academics. One thing to remember in teaching anyone anything is that most people can't handle more than one or two layers of instruction at a time. The problem is that to be a good flyfisheman you have to do about 10 things well at the same time. So here's how I like to simplify it:
I start by getting out 12-15 feet of flyline (just enough so the person can feel it load the rod when they cast properly), with no fly and no leader attached, and laying it straight ahead of me in the grass. Then, I hand the rod to the beginner. To simplify, I first I tell them to forget about their left hand. I just want them to learn how to load the rod. Then I tell them that the key to flycasting is line control, which means they have to learn how to use the energy from the moving line to load (bend) the rod, then use the loaded rod to get the line moving again. They have to try to FEEL the rod load at the end of each casting stroke. This is the key to getting past the floppiness of those first casts, feeling the rod load. I haven't yet tried taking the Zen approach and blindfolding anyone yet, but doing so might really help simplify the problem of casting to the one critical aspect - feeling line control. If the beginner can learn to FEEL line control rather than making it a dizzying array of arm positions, mechanical complexities, timing considerations, etc., then he can focus on the most important thing - the fish he's trying to get his fly to. There's plenty of time for refinement after he's learned to load the rod.
A helpful hint that addresses a common misconception that often hinders beginners: Casting is not a fluid motion. Want floppy casts? Then make casting a fluid motion, because when it's fluid you'll just trace loose 'S' curves in the air. To get the rod loaded, you've got to think of casting as strong thrusts interspersed with statuesque pauses. It's these pauses that freak out the beginner. He thinks that the line will only stay in the air with a casting motion full of sound and fury, when all he really needs to do is give it a firm thrust each time the rod loads, then - the hard part - WAIT for it to load again. Get him to see that, and you've gotten him a long way towards good casting.
Once the beginner moves on from just waving a section of line in the air and begins involving their left hand, another misconception often needs to be addressed. Too many people have read or watched "A River Runs Though It," one of my favorite stories but one which doesn't always give the best actual flyfishing advice. The idea of learning to cast to a metronome is ridiculous, because every time you let out more line you need to allow more time for the line to lay out. There is a certain rhythm to casting, but it is not a regular rhythm - the time between each thrust must get longer. What is the constant? Feeling the rod load before starting the next false cast. I've found I often have to talk a beginner through this misconception before he can begin understanding proper timing.
-Shawn