you want to hold your pick so that your thumb just completely covers the tip of the pick when you look at it in your hand. The idea is to hit the string with the pick and then mute it, so to speak, with your thumb at the same time.
This action takes place really fast, like in the beat of a humming birds wings. It takes days of practice, but once you get it it will be so easy. The more distortion you use the easier it is to get artificial harmonics.
Practice slowly and when you start getting it, do it all the time for a while, in time you won't even have to think about it.
Sixx
PS Vibratto w/ pinch harmonics really sticks out.