When I was growing up learning, Zakk Wylde was my favorite guitarist and Randy Rhoads was another huge inspiration. Not surprisingly, doing pinch harmonics was a *must-do* for me very quickly. I did them all the time just because they sounded cool, while playing along w/songs that had them, or just threw them in for the hell of it. Eventually you get to the point where you don't even have to think about it.
It's tough to explain without being there with you, but I found this pic on Google which shows what I'd want to show you. Make sure you're holding the pick like this:
The pinch harmonic is made by using a downstroke and brushing the outside of your thumb (at the thumbnail) across the string as it's picked...THEN MOVING IT OFF THE STRING IMMEDIATELY. Otherwise you'll muffle it. The process is incredibly fast so I'd figure speed is the biggest issue for a lot of people. When you try it out, just keep picking at it until you get it. The main thing is: a) pick the string, b) brush the side of your thumb as if you were creating an artificial harmonic on an open string, c) don't muffle the string