In the classical guitar world, artificial harmonic usually refers to a low-order harmonic (i.e. one in which the frequency produced is a low integer multiple of the 'base' note, most often a simple octave) which is performed on a fretted string.

Assuming you're playing 'right-handed' (reverse the instructions if not) the left hand frets the string, and the index finger of the right hand is placed gently on the string at the appropriate place, while the right-hand thumb plucks (though it can be plucked with the another finger, usually the third, if a simultaneous bass note is required).

The plucking should usually be done on the side of the harmonic 'node' (where the finger rests) which is nearest the bridge, in order to maximise the volume of the note produced; though, as the string is all vibrating at the same frequency (just as it does in a 'normal' harmonic) the pitch would be unaffected by plucking on the 'wrong' side.

For example, fingering the 3rd fret on the top E string with the left hand, resting the index finger of the right hand on the same string just above the 15th fret, and plucking with the thumb, gives a G exactly one octave above the G that would be obtained by plucking the string without the harmonic.

On a classical guitar, this can give a delicate 'musical toy' effect, as, for example, in Agustin Barrios Mangore's piece El sueno de la Munequita (The sleep of the Little Doll).