Not many people consider how the markets work.
HOW IT WORKS:
The LCN stock market is based on your individual game instance (client side). It looks at what you are doing, what it is affecting, and adjusts the stock prices based on that.
Easy to manipulate it in your favor by investing in one company, and destroying it's rival (will still take a good bit of work and destruction).
It's downfall is that you don't know how the NPCs in the game act, so investments based on consumer habits are a little harder.
Pay attention to everything from what characters say in cutscenes to what the people on the radio are saying. They usually drop hints as to what's going on, or what people are doing so you can analyze it and make investments.
HOW IT WORKS:
Bawsaq gathers data from you, your friend, that kid in the COD lobby who's mother you just claimed to have fornicated with, everyone who has this game, an internet connection, and is playing, it takes all that data, and bases itself on all of that data.
Easier to predict stocks based on consumer habits. This is because we ourselves are the consumers. I couldn't tell you what the NPCs are doing, but I know that, typically, players are going to be buying guns, buying cars/boats/aircraft, and upgrading their vehicles. So logically, the sound investments are in those areas. The more things people buy, the more valuable the stock.
Not as easy to influence in your favor (unless it is tied to a mission like assassinations) due to it being a larger pool of influences.
PAY ATTENTION TO THINGS GOING ON IN THE REAL WORLD!!!! Since it is a collective stock market, expect stocks on commonly used things like guns and cars and such to go UP at times when more people can play like weekends and holidays. Also pay attention to times like when multiplayer rolls out. Stocks are bound to go up then too due to everyone starting up their gangs and stocking up on weapons, ammo, and vehicles to play around with. They will go down after everything chills out, but any major event like that is going to boost play times and money spent on such items.
That's about the best explanation and tips I can currently give. Feel free to copy and put into the OP.