Natural harmonics
While playing natural harmonics, the left hand is only being used to mute a string. So when you play any open string, and mute it slightly above the fifth, seventh, twelfth or nineteenth fret, you will hear a natural harmonic.
In order to let the harmonic sound as long as possible, you should take away your left hand immediately after playing the string.
The closer you keep your right hand at the bridge of the guitar when playing the string, the brighter the flageolet will sound.
Artificial harmonics
To learn artificial harmonics, it is important to learn natural harmonics first.
An anrticicial harmonic is nothing more than a natural one, except that you don’t make use of the open string. For example, press the second fret like you would do normally. Then you use your index finger on the right hand to mute the string on the 14th fret. Play the string with your ring finger.

Have a look at Tommy Emmanuel playing the song ‘Somewhere over the rainbow’. In the intro he makes use of a lot of (artificial) harmonics, and plays ‘normal’ notes in between them.