Another way of achieving
artificial harmonics on a guitar is through
tapping. The technique is similar to both standard
tapping and the
classical technique described
above.
Finger a note with your fretting hand (left hand for righties). Then tap the string quickly with your playing hand an appropriate distance from the fretted note (12 (octave), 7 (octave + fifth), 5 (two octaves), or 9 (two octaves + fourth) frets away are good (see harmonic), ranked easiest to hardest for sounding purposes), right over the fretwire of the appropriate fret. For example, to tap the octave harmonic for the third fret of the A string, you would tap quickly on the A string over thefretwire between the 15th and 16th frets.
This technique should be performed quickly; what you're trying to do is bounce the string off of the fret so that the harmonic sounds, not hold it down so that that fret's note sounds.
This gives a sharper sound than touching the harmonic would.
This can also be performed with a pick by tapping with the edge of the pick in the right place. This may be easier, since the edge of the pick is smaller and can be more accurate.
On a side note: the technique that ferrouslepidoptera describes is also referred to as "pinch harmonics" because of the way the note is sounded: the thumb pinches off the note at the appropriate node.
For a modern example of this, listen to Van Halen's instrumental "316"; Eddie Van Halen finishes off the piece by tapping an arpeggio.
Another advantage of the artificial harmonic is that it can be bent; node the harmonic point and then bend the string with your fretting hand for some interesting results.
Another way of fingering the harmonic is by using the opposite hand configuration that JK mentions: holding the fingers as if one was holding a pick, touching the string with the playing thumb, and playing the harmonic with the index finger immediately behind the thumb.