Basically, in the second part of the book(Post exposition, when you unlock Qi) click in "activities" during free-roam, then click again in "teaching lessons" and spend the 3,000 gold, this will unlock the most lucrative operation in the book so far. You'll only be able to profit from it in the next free-roam after spending the money renting the location, where you'll need to click in activities & Teaching lessons again. There'll be a primary and secondary CHA checks that are intrinsically related to how much money you get per turn. If you fail even the primary check, your base value is 10. If you pass the primary check, the base value is 20. And if you pass the secondary check, the base value, obviously, is 30.
The money gained per-turn through this activities happens under the calculation of; Base Value(Defined by which check you passed, as explained above) multiplied by your prestige, that's why prestige is important.
So, for example, if I have 151 prestige and passed the secondary CHA(charisma) check, my earnings will be 151 X 30, resulting in 4.530.
The strong point of teaching lessons is that you gain a passive earnings per-turn(Such as the clan's stipends, sect stipend, earning from the restaurant...etc) that are also based in prestige but instead of a fixed value they're rounded. And along this passive earnings per-turn you can, in every free-roam, click in "activities" and "teaching lessons" to gain the fixed Prestige X base value defined by the check passed.