Ok, I am not a CCI and have never taken lessons. I have been given pointers by some good casters.
I have a fishing cast from years on the river which suits me fine.
I was looking for James Reams(a bamboo rod builder) and ran across this which I enjoyed watching.
It is very simplistic and I think is a good film for any fly caster that isn't an expert.
There may be other techniques that are now used for teaching but for me this follows what I have learned and mostly apply.
If you are just getting into fly fishing, many novices enjoy the casting because they can do that at home and on the river and it helps bide one's time when they aren't catching fish.
I cast to fish and not fish to cast. Big difference. One will figure that out as they progress in the sport.
Hope this might help someone who is having trouble. It does take time and for some of us, Lots of It!