Holding and Positioning the Knife
Hold your chef's knife with your dominant hand. Use your main hand to grasp the handle of the knife on the blade with your index finger and thumb. Your fingers and thumbs should be in front of the bolster, the thick part of the blade that it touches the handle. Try not to let your index finger pass through the top of the blade.  Grasping the blade gives you more control.
Although you can still cut while holding the entire handle completely, there is no optimal range of movement.
The index finger and thumb should look like they are pinching the sides of the blade.
Use your subordinate's hand to form a paw. Hand that does not hold a knife should hold the food you are cutting. To prevent the knife from cutting your subordinate's hands, bend your fingertips toward your palm so that your hand forms a claw. Place your claw-shaped hands on the food you are cutting so that the food does not move or slide. 
This may not be natural when you start practicing, but it is the best way to prevent kitchen accidents.
Protect the thumb on the subordinate's hand. It's important to use your assistant's thumb to squat, so you're unlikely to cut it. The knuckles on the thumb and fingertips should be closer to the blade than the fingertips. In this way, if you cut quickly, your knife will only touch the knuckles instead of cutting your fingertips. 
Keep your thumb hidden while practicing. If you find your thumb sticking out while cutting, stop and repeat your thumb. Practice slowly until it becomes a habit.