Start out by holding the Jews harp with the "L" curved part facing away from you. This works best if you point it at a small dog or cat or even another person.
Now, grip the edge of the rounded end firmly with your index finger and your thumb like in the second picture. You do not want it to slip or move at all so apply about the same pressure as if your were Vulcan neck pinching someone.
Make sure the no part of your hand or fingers are touching the thin piece of metal in the center, because it has to vibrate freely.