In my experience with the USPTA, much of the focus in a particular lesson seems geared toward getting to the most fundamental problem that needs fixing and also making the very most of a given amount of lesson time. While they don't preach a strict formula, the 'PTA promotes several elements that they have found to contribute to a productive and enjoyable learning process on the courts in most settings.
The best thing that I learned in my certification process was to quickly identify the upper limit of the skills of my student so that the lesson isn't too easy or too hard. For example, someone may have a solid volley, but when you make them hit the same shot with some movement and it breaks down, you have a limitation to work on. If a drill is too hard for a player, you need to recognize that in a hurry and adjust your approach or the lesson will be almost useless for that student. I know that this is sort of mastering the obvious, but the certification review course that I took was really helpful toward managing this issue.
While I didn't learn a specific process to teach a forehand for example, I did learn about stroke analysis to help identify good and bad mechanics. I recently took on a student who hits two-handed on both sides and while I didn't want to talk her out of that style, I did need to correct a significant grip problem on one side so that the stroke could fundamentally work. Different teaching styles including favorite drills and games are probably common among teachers regardless of their certifications, but I think that the USPTA wants its teachers to generally help players to improve what specifically works for them.
