Hey Vernon great question. Stocks are a very interesting thing to follow but I would preface it by saying it can also be very risky. I invest personally, but a good thing to think about is that you could potentially lose all of the money that you invest. So I would only get involved if you are able to take that risk and know that there is no guarantee that you will make money.
That being said, there are a few websites out there that make buying/selling stocks relatively easy. I personally use Fidelity but other popular ones are E-Trade and Charles Schwab. They all have good statistical tools built in to help you compare stocks.
As far as what stocks to buy, I would first recommend finding an industry that you are interested in, and start paying attention to headlines for those companies. That way you can easily follow the news and see if something good/bad is about to happen to the company. If you watch channels like Fox Business or CNBC, they also provide good coverage on stock opinions and how the overall market is doing. I would recommend to just sit back and follow the stock market either on TV or online for some time before investing.
Personally I have never traded penny stocks. My view there is that the likelihood of large growth is slim and they may not make money at all. But you could potentially find a few good ones with a lot of research.
Something you may look into is investing in what are called ETF's, which follow either a group of companies within the same industry, or follow a specific index such as the NASDAQ, which is a selection of a bunch of companies from different industries. The reasons I mentioned ETF's are that they are not as impacted by one particular company doing bad. For example if you had a bunch of stock in Apple, and Apple's stock goes down, your entire investment is impacted by that. But if you have an ETF that includes Apple among other companies, it helps diversify your risk. Also sites like Fidelty have ETF's that you can buy through them that do not charge you a fee each time you purchase shares. An ETF that follows something such as the NASDAQ can be a safe bet over the long term too, since the overall chart for the NASDAQ is positive over time, even with recessions factored in.
Anyways I hope that information helped. The unfortunate thing about stocks is that it's hard to be certain about anything, and with your own money on the line it is not something that everyone should risk. Everyone has an opinion but essentially no one knows for sure what will happen. That being said, the more homework you do on the stock market, the better your chances of success can be.