The balance or blend of the fundamental and harmonics in relation to each other determines the instruments "tone". Every guitar or instrument does not produce the exact same tone because every guitar produces a different balance of harmonics.

First Harmonic - String vibrates in two equal lengths giving artificial harmonics one octave above open string

The easiest way to play open string harmonics is to place your first finger over the 12th fret covering all 6 strings. Next lightly strum the strings and as soon as you feel the strings being struck remove your left hand off the 12th fret. This will take some practice of course if your new to this but keep trying and you will get it.

Second Harmonic - String vibrates in three equal lengths giving artificial harmonics one octave and a fifth above open string

To play the second harmonic place your first finger over the 7th fret or 19th fret and do the same as I mention in the first example

Third Harmonic - String vibrates in four equal lengths giving artificial harmonics two octaves above open string.

To play the third harmonic place your first finger over the 5th fret or 24th fret and do the same as I mention in the first example

Fourth Harmonic - String vibrates in five equal lengths giving artificial harmonics two octaves and a major 3rd above open string.

To play the fourth harmonic place your first finger over the 4th,9th or 16th frets and do the same as I mention in the first example.

Fifth Harmonic - String vibrates in six equal lengths giving artificial harmonics two octaves and a fifth above open string.

To play the fifth harmonic place your first finger right after the 3rd fret. In theory it's fret 3 and 1/3.