An outline of a DM training manual

Present-day D&D practice may not admit of a procedural manual, but ours might, no?

An initial chapter might explain the importance of having a place that you control as the game venue (generally your own house), explaining why playing in a public place is liable to have too many distractions, as well as giving advice for keeping the fridge stocked, ordering food ahead of time and all that jazz. Simple stuff, yes, but things that a noob might not think to do for an art form with a strong component of people management.

That last needs a whole chapter too: Paying attention to players' emotions. Stepping in to resolve conflicts that are getting out of hand w/ techniques like making everyone go for a walk to cool down tempers. Praising players for good planning, good cooperation, clever use of abilities.

As a segue from that chapter to the rest, you could talk about the DM's behavior at the table, speaking clearly, speaking firmly, committing to decisions, giving brief responses rather than whole paragraphs of box text style description. Might not be enough of a whole chapter, might have to be woven into the rest.

Then the study and mastery of your game's existing rules. This would be fraught as many games don't have all that many rules to study. But it would be a good place to introduce the virtue of not taking anything of the rules say for granted, and being prepared to maintain one's own set of extensions and changes to the rules as the DM slowly makes the game his own. We could also introduce the concept of self-play here, as a way to bake the rules into your brain.

Then, the importance of studying real-world topics, with an eye to the situation where the game lacks rules for something, and the DM needs to familiarize himself with that topic sufficiently to be able to bring that thing under the game's aegis. This would be a fat chapter indeed. You can't cover every topic that pertains to D&D, because every topic pertains to D&D, from history to medicine to vexillology to sex to painting to political economy. But you could take a couple example areas of human endeavor and show how to break them down along the lines of a sage study. Or take some shoddy rules, show where they fail, where they're logically inconsistent, what bad incentives they create for players -- then make them better. One example of that might be demonstrating why it it's not a good idea for skills to be rolls, rather than being abilities players always possess. You've written that argument more than once. (I'll admit this might be a skill that can't easily be taught, or at least, is hard to learn through anything other than trying and failing, trying and failing...)

Then there are creativity exercises. Making oneself write one sentence or one paragraph or one page about the same scenario. Maybe you'd go in the other direction, starting with a page of description and showing how to condense it down to just what's essential to give the players a sense of place, as well as details that might compel them to act or frighten them into indecision.

I can't claim that one can really learn D&D from a manual. Like any art form, especially one with an improvisational component, books will only take you so far and practice is 90%. But at very least, I'm confident that apart from How to Run, I have never seen a "DM's guide" for any game that tried to explain how to do these things, rather than just gesturing at them.