Here's the way I do an artificial harmonic. It takes practice, but when you get it right, it's one of the best methods.

I'll give an example to make it easier:

- press and hold the 12th fret on the high E string

- hold the pick between your thumb and middle finger

- with your right index, touch the string at half the distance between the 12th fret and the bridge. don't press, just touch

- now pick the string, and as soon as you pick remove your index finger

You should get a high pitch sound (actually the equivalent of the 24th fret)

The artificial (and natural) harmonic raises the note by an octave (12 frets).

The same can be done on any fret on any string. It's harder to pull at higher frets, but in theory you could go as high as the 34th fret with a 22 fretted guitar.