As far as research.. there are lots of websites, books, and tools to get you started. One of the first things you should become familiar with is chart reading. This way you can glance at a chart for about a minute and instantly have a fairly broad view of the stock, it's history, trading patterns, and possible profit potential.Once you can find stocks that "look" good on the charts, you basically just need to do a little more research on the company. See what current news releases are out there, check out a few of their latest SEC filings, see if the general trend is positive or negative regarding the company.
The rest is all up to the market and a little bit of luck to make you some money
Regarding how to invest your money, I can't really tell you how to put it to work best, but you will definately benefit much more buying a stock or two and holding it rather than trying to time your plays in and out every day, eating into your profits with commissions.
There are a lot of stocks out there that can make you 10-25% in a week or two. You may want to find one and set some goals like that. I mean that 500 dollars could turn into 600 dollars in a week or so.. maybe more, maybe less. But you would be a lot safer to buy and hold at least for a few days and then sell, taking some of that money and moving on.
Depending on how much you have to spend, you may also want to consider splitting your money up. Maybe invest half into a solid growth stock, not a penny stock. Something that you can keep in your portfolio for a few months or a year, kind of a safe haven. Over time, that money too can possibly see a good 25% in 3 or 4 month's time.
This way you have a bundle of money working for you safely, while you are getting used to trading pennies. Think of it as a high interest bank account (with the possibility of it still going down).
But with limited funds, the general rule of thumb is you want to trade less, and hold more. If you make 10 trades in your first month with your 500 dollars at 10.99 commission, you're spending 110 dollars that month alone just to try and turn your 500 bucks into something much more. That means you'd need to get a 25% return just to break even... or, you could trade just once or twice in a month, spending 20 bucks, and retain almost all of that profit.
It is a tangled web with so many decisions, and things change so fast once you actually get your money in the market so nothing is ever set in stone. I would just advise to trade less and build up your portfolio value slowly, because unless you sink your 500 bucks into a stock that is super lucky and gives you a quick 100% in a day or two.. you will be quickly discouraged.