The share market is one of the most elaborate, and profitable, aspects of the game. Here are a few tips just to get you started:
1. Dividends from the country portfolio go to your country. Dividends from the investment fund portfolio stay in the investment funds. Dividends from an enterprise portfolio go the CEO.
2. The country portfolio only owns shares of your state corps that issued public shares, or of CEO public corps that your country nationalizes. The country portfolio can't buy shares of corps not owned by the country.
3. You can have your CEO buy shares of your country public corps, and even get majority control. If your CEO moves any of its public corps from your country to another country, your country continues collecting dividends from its shares of those moved corps. (That's a nice way for your country to earn income from corps that aren't even located there.)
4. Investment fund automation is quite smart. It buys low and sells high, based on P/E. (They buy when the P/E is up to roughly 12-15, and sell when the P/E is over roughly 12-15.) However, some of us sometimes manipulate the P/E of different corps for various reasons. So it's debatable whether to trust the automation.
5. If you turn the investment fund automation off, a good use for investment funds is to buy shares of your CEO's public corps. That helps prevent other players from getting control of those corps. That's probably the best use for investment funds.
6. Taking your country corps and CEO corps public is a great goal because that allows you to upgrade them more. It's best not to take them public before they're upgraded to 200; that way you'll be able to keep adding cash during the costly upgrading to 200. Also, it's best not to take them public before they have a P/E of 15; that way funds with automated buying hopefully won't be trying to buy shares that you may want your investment funds or CEO to buy.
7. Share trades are executed only on certain days of each game month. Currently, trades are usually between the 6th and 25th, with one or two "holidays" in between and some fluctuations in dates. That's why the share market often seems frozen.
8. Experiment a lot. The share market is an amazing and lucrative part of the game. The more you experiment, the more workarounds you'll find to exploit.