There is no fixed number of hands that will tell you if you're a winning player. However, you can estimate the likelihood that you are a winning player as a function of your observed win-rate, standard deviation and hands played.
This site will do it for you without making you learn any formulas.
http://pokerdope.com/poker-variance-calculator/
As an example, if you play 10,000 hands with a true win-rate of 0 BB/100, crushed over the sample at 20 BB/100, and had a SD of 80 BB/100, the probability of having this result given the premise that we are a breakeven player is .6%, so it's 99.4% likely that we're a winning player.
You can find all these stats in PokerTracker.