There are different methods of starting the powerball gyroscope depending on your skill level.
The beginner method uses a string that comes with the ball. Insert the string into the hole of the gyroscope and wind up the string by turning the gyroscope in the ball. Then as fast as you can, pull the string out to spin the motor. Then accelerate the ball by rotating your wrist in a clockwise or counter-clockwise motion. For beginners, it will take a few tries to get the hang of it.
Once you are fairly good at accelerating the ball, you can move onto the more advanced starting methods. These methods start the powerball's gyroscope at a slower speed so good timing and skill are required. Hold the powerball in your hand and press the gyroscope against the palm of your other hand. Then move your palm to spin the motor and begin rotating the powerball to gain speed. You can also start the ball by using your thumb or by swiping the ball against another hard surface.
This video shows a flick start, though he makes it look easier than it seems.