This is a good question. Of the 3 basic short game shots, putting, chipping/bump&run and pitching the pitching motion has the most moving parts and for most people is the most difficult to learn.
Everyone teaches a little differently, but for me I normally teach a lot of chest rotation on the forward swing, very similar to how you would turn your chest to toss a soft ball underhanded from your golf posture.
For chipping/bump & run I teach a more linear concept. Stance is very square, weight on front side, ball positioned off of back foot, club works almost straight back and straight through with very little to no wrist hinge or club face rotation. The results are very positive and the students do not have much difficulty achieving this move.
What I have done through the years for people that can not pitch the ball in the traditional manner is to modify the chipping motion. We stick with the feeling of straight back straight through but we move the ball position from back in the stance to more forward, we use more loft (SW or LW vs/ 8 or 9 iron) and we incorporate some wrist hinge.
It is not a full proof system, the ball doesn’t come out as high as traditional pitch shot and the leading edge is more exposed, which can lead to digging, but the students that I have done this with feel much more confident in this approach versus struggling with trying to learn it the traditional way.