I'm no expert, but I'll try to clear some things up.

Natural - played by having your fretting finger lightly touching the fret (as in the actual wire) on the 5th, 7th, 12th, 17th etc.....

Pinch - Can be played on any position on neck, much harder than natural. Press down on the fret (as if you were to play the note), then choke up real hard when you pick so your thumg and index finger rub against the string as the note is picked (I hope that made sense), the result is a wild screaming pinch harmonic! The pitch of the harmonic depends not only on the fret position, but also where you pick the note. This is why it is easier to pull off a pinch in certain spots.

I haven't had much experience with artificial. I used to think that the two mentioned above were the only kind. Its not my fault - in Rock Guitar For Dummies Pinch and artificial are used interchangeably. The same goes for Zakk Wylde's lesson on pinch harmonics. But most of the people on this site say otherwise, so I trust 'em.

Peace Out!