Gary, I'm not much of an expert but I can at least answer your question.
It all has to do with proper positioning and pressure of the teeth against the jew's harp. In cross-section, the two bars of the jew's harp you press against your teeth are diamond shaped. Your teeth must be separated enough so that the inside lower and upper flats of the bars of the harp can be pressed against the biting edges of your front teeth. The lips should more or less seal above and below the harp. The teeth must not clamp down on the harp because that will force the two bars together and the twanger (I think it's properly called the tongue) will clack against the bars. Also make sure the hand you are holding the harp with doesn't press the bars together. This is more of a problem with some harps than others, as some have more flexible frames.
Be sure to press the harp firmly against your teeth so the vibration will be dampened by the mass of your skull (no, I'm not calling you hard- or thick-headed). Some people seem to be more sensitive to this than others, though. I think you've got to have good strong teeth to play the jew's harp.
Go to the web site Wolfgang mentioned above and snoop around a little. There are some good instructions there somewhere that may be more clear.