The basic idea of how to make money in the stock market on AS is one of two ways: Shares and Dividends. I'll go through both of these.
Shares -- On AS, you can buy and sell shares at up to 10% of the difference of the Current Stock Price. The Current Stock Price can be found on the right hand side of the stock page. The "Current" is in bold letters. This is the current price. Now, to buy shares in this stock, you have to bid on them. On the bottom left of the page, there is a place for you to put in how many shares you want, and the maximum price you want to pay per share. The money will be taken out of your bank account as soon as you submit the bid, so be careful with how much you are wanting to bid -- though you can cancel a bid immediately and at any time.
After you have bid on shares, you have to wait for a couple things. First, you have to wait for someone to sell shares. There might be someone already selling them. You can check to see how many shares are up for sale and the price they want. If you want 100 shares at $100, and someone is wanting to sell 100 shares at $100, then you will buy those shares the next time the game goes through a "Execute Stock Exchange Trades" on the game status page.
If, to continue the example, you wanted to buy 300 shares at $100, and someone is wanting to sell 300 shares at $105, you won't buy any of the stocks. You have to at least bid as much as the amount they want. If you bid 300 shares at $100, and someone is wanting to sell 300 shares at $95, you will buy 300 shares at $95. They get what they ask for, but you don't pay extra. That money will be refunded when the stock purchase goes through. There are a dozen other examples I can go into here, and it's not really worth it (but I will if someone wants).
Okay, so now we got stock. You can look at your stock under 'Subsidiaries and Portfolio' on your top menu. If you click on that, you will bring up your stock listed under 'Shares in other enterprises'. It will list there how many shares you have, Note the "Book Value". That's the price you've paid total for all that stock. That is what you have invested in the company. Now look at the "Market Value". That's the price your stock is worth using the Current value mentioned above. Remember that the price can fluctuate 10% in trades. So if you want to sell the stock, and make money at it, you want to make sure your "Market Value" is more than your "Book Value". If it isn't, you are probably going to lose money when you sell your shares.
Now to sell shares, it's just the opposite of above. You put the shares out there, and put a price you want to sell them at. Again, it has to be within 10% of the Current price, otherwise the system will reject the offer. Once it's on the market, people can buy it right up. Voila. That's how you make money with shares.
Dividends -- Dividends are something else entirely, but they are still based on shares. The percentage of shares you own in a company, along with the percentage of all the other share-holders, is listed on the stock page. The percentage listed is the percentage of the total dividend you will get every week, so long as you own the stock. The dividend is calculated as 15% of the company's weekly profit. So if a company profits $20 million, their dividend payout to all share-holders is $3 million. If you own 10% of that stock, you will get $300,000 when the company profits $20 million. If you buy more shares, you will get a higher percentage of the dividend. If you sell off shares, you will get a lower percentage. So it is good to invest in a company that is making money. The more money the company makes, the more you get paid on dividend. Note that if a company doesn't profit during a given week, no dividend is paid out.
Dividends are one of the two ways companies can transfer money back to a holding. Because after the IPO, the holding company (or more precisely, the parent company) holds onto 80% of the stock, and will get 80% of the dividend. In the above example, that's $2.4 million out of the $3 million. The other way to transfer money is for one of the companies to buy a plane and use the Asset Transfer function.
There are a lot of other little nuances and quirks with regard to the stock market. If you have any other questions, feel free to ask. :)