If I am guiding a true beginner I teach them one cast at first; the "water cast."
I instruct them to cast down river and let the line stretch out then all you do is lift the rod up vertical to the 1 o'clock position behind behind your head and shoot it forward. This will work well where I start at the beginning of the day. After that they slowly but surely start to false cast on their own without any command from me. And as long as they are getting the flies where I tell them I never say a word. I have noticed that if I speak up about some technicality in their cast it almost immediately gets worse than it was. If they are constantly messing things up I will just remind them to do the water cast.
For the most part I have no problems with fixing birds nests every now and then or getting flies out trees. That is why I am there. With all they need to learn in one day; casting, stripping, mending, setting the hook, and getting a larger fish on the reel, anything technical I can leave out of the casting portion I do. Keep it as simple as possible.
I think less input in the beginning is always better. If a person is really interested in fly fishing they will figure out their cast enough to be an effective fly fisher. Then, if they decide they want to be able to double haul 80' of line then they will get a lesson from a FFF certified instructor and hone the skills to a fine point.
I think a lot of people just catch a natural rhythm by instinct...
The sport is so royal that there is neither gentle nor villein, if it knew of it and loved it well, who would not be more honoured for that reason by all who understand it.