Bottom line up front: there are many different theories about how to succeed in the stock market, and the truth is, most people are not going to become a stock market millionaire.  However... there is no reason why you can't be the exception, right?  Someone has to become the next Warren Buffett!  Why not you?

The # 1 Rule: Don't Lose Money.  You will read this in many books about stock market investing, and it is an absolute key.  If you continually lose money due to poor stock picking (which results from poor research and poor education), they you've lost as soon as you've begun.  Take great care to not just through your money at whatever seems like a fancy stock purchase, and be sure to know when and how to cut your losses.

Beyond this, to succeed, you should practice.  Some people recommend that you use a 'fake money' account to trade for practice, but in truth, without the emotion of "I am actually losing money!" or "Wow, I just made some money!", you won't learn how to manage the most important tool in your trading toolbox: your emotions.  This is why practicing with $10 of real money on the line will probably serve you better than trading with $10,000 of 'paper trading' money.  While paper trading has its usefulness, ultimately, you will learn the most when you have your skin in the game.

Next, learn about as many different strategies as you can, and find the one(s) that work best for you.  There is long term stock trading, day trading, short-term trading, precious metals trading, bond trading, options, puts, saddles, straddles, butterflies, and the list goes on and on.  The more you learn, the better choices you'll be able to make. 

Finally, don't give up and keep learning.  Learn lessons from each failure, and from that failure, create a rule.  From your next failure, create a new rule or revise the old one.  Add more and more rules as you practice.  Know precisely why you've purchased a stock, and why you are selling.  Know when you will sell, and when you will purchase more.  The more you learn, the easier stock market investing will be.