To be honest, the title of this lesson video is a little misleading. Although this technique does create more overtones, what is really being controlled is which strings are being aloud to vibrate.
The easiest way to get started with this concept is to allow the note an octave above the note you are playing to vibrate. It sounds more confusing than it actually is, trust me. Check out the explanation in the video and let me know if you have any questions!