Touch the ball with your fingertips, not your palm. Don't slap the ball with your palm. Rather, try to handle the ball with the tips of your fingers. Spread your fingers out across the surface of the ball for a wider, more balanced contact area.
Get in a low stance. When dribbling in an upright posture the ball will have to travel from your upper body to the ground and back again as it bounces, leaving it wide open for a defender to steal. Before you start to dribble, get in a low, defensive stance. Spread your feet shoulder-width apart. Bend your knees and drop your hips back slightly (as if you were sitting in a chair). Get your head up and your upper body mostly upright.