Buy low, sell high. You can make or lose a lot of neopoints. "Wheel and deal on the Neopian Stock Market! With the help of Nigel, the Commodity Broker Chia, assemble a stock portfolio and start buying and selling your way to stock market success!"
The Neopets stock market will not allow you to buy a stock that is worth less than 15 neopoints per share and you can only buy 1000 shares a day, although stocks you already hold can drop below that price. Most wise Neopets investors buy new stocks around 15 to 20 NP. Don't buy stocks that are more than 20 NP a share, because your goal is to make neopoints. Buying one that is already at 30 or 40 NP doesn't give you that much room to grow. Buying 15 NP stocks regularly should mean that you will have one or two stocks run up to 30 NP or even 60 NP a share pretty regularly also. When choosing stocks to buy, see which ones in that price range are stable or increasing; don't buy one that has dropped down that day. Don't buy small amounts of shares; you will pay a flat commission of 20 NP for each transaction, so buy at least 500 shares at a time, and preferably the maximum number of 1,000 a day. Sure, the more shares you buy, the much more it costs (depending on how much each share costs), like buying 1000 shares that are each 15 NP, making it 15,000 NP to spend, but it can increase to a big amount throughout time.
When buying shares to sell them for a bigger certain amount, it can take a very long time, usually 3-8 real life months for it to be sold for a lot, so doing this will have to take a lot of patience.
When to sell is by far the most common question and the most difficult to answer. It's really up to the individual, depending on your personal goals, and how many neopoints you have in the bank.