I'm just about done with it, here's what I figured out:
For shareholders, there's a rock paper scissors element to it that works in two ways: the questions they ask and what they are interested in. For the questions, picking the right kind of person that wins the RPS triangle will break all three shields, picking the same will break two, and picking the wrong one will only break one. The questions are color coded like the triangle. Once the shields are broken, pick the right person to damage them once again based on the RPS triangle, but note that the person may have asked a question in a different category than what they actually are.
You can preview what the board will look like ahead of time, so pick a team that has both a diverse set of symbols (the little person icon, the money stack, or the building icon on their card) and a good ratio of stats to costs (each person has a different listed amount of damage/toughness and a point cost associated with using them to answer).
Leveling up your team will also level up their shareholder stats and may control how big your point pool is to call on them during the meeting (I'm not sure of that, but my board is now all max level and my points seemed to top out at 100).
As for the actual management itself, it's fairly straightforward. People have businesses they are best suited to and roles within there that best use their stats; just look at which role will use which stat (except for the far left slot, that always uses all three), arrange your people accordingly, and upgrade your business's sales volume when you can hit most of the stat targets.
Thank you for this! I was able to make it through the shareholder meeting! Things are looking up with this management game at last. XD