This exercise is from my new book Classical Guitar Technique: Essential Exercises, Scales, and Arpeggios. The 122 page book includes: Practice Routines, Tips, 100 Open String Exercises, 120 Giuliani Arpeggios, Scales, Slur Exercises, Shifts, Finger Independence, Barre, Tremolo, Common Harmonics, and much more.
Natural harmonics (left hand harmonics), as they are commonly named on guitar, are played by lightly touching a left hand finger directly over the fret (the actual metal fret) and plucking the string as normal with the right hand. Do not push the string down to the fret, simply place the finger lightly on the string and remove it after plucking it (allowing the string to vibrate).
Artificial harmonics (right hand harmonics), are played by lightly touching a right hand finger directly over the fret (the actual metal fret) and plucking the string with a different right hand finger. This can feel awkward at first until you become confident and comfortable with the technique. My personal preference is to touch the string with the i finger and pluck with the a finger, but other combinations are possible.