| Here's some basic starting knowledge about harmonics.
There are two "types" of harmonics; Natural and Artificial. They are identical in all but the following respect: harmonics are called 'Natural' when they occur on open strings, and they are called 'Artificial' when they occur on fretted strings.
A harmonic occurs when the string is vibrating and a 'node' is touched. A node is a point along the string which corresponds to a fraction of that string's length. For example, you can touch a node at 1/2 the length of the string, 1/3, 1/4, etc, and these will each give a different harmonic.
*NOTE*: many harmonics are found in several places. If you touch a node that is 1/3 the length of the string (ie at the 7th fret), it means the string is vibrating in 3 parts. So there are two different nodes that give this same result; one is at the 7th fret, the other is up at the 19th fret. Each node is the same distance from the 12th fret (the middle of the string), and from the end of the string (the nut at one end, the bridge at the other).
Playing Harmonics
To play a harmonic is different from fretting a string because you don't push down. Instead you just touch the string lightly at the node point. Pluck firmly; playing near the bridge and with plenty of mids in your sound will give you a better chance of the harmonics ringing clearly.
When using Natural harmonics it's generally a good idea to use your left hand to touch the node. When using Artificial harmonics, it becomes trickier, but there are four main ways to reach the node. These can all be used for Natural harmonics too, but they start to become necessary when using Artifical harmonics.
1. Stretch with your left hand. This may or may not be possible depending on hand size, and how far from the fretted note the nodec is.
2. Touch node with index finger of right hand, and pluck with remaining fingers. The "Steve Bailey" method.
3. Touch node with thumb of right hand and pluck with remaining fingers. The "Jaco" method.
4. When using a pick, pluck over the node, and continue the wrist motion such that the side of your thumb ends up touching the node.
Number 1 is the best one to use in the examples I have given, because they are all an easy reach. For numbers 2-4 you have to know where these nodes lie at the opposite end of the string. This goes back to what I mentioned before; many harmonics can be found in several places. When touching the node with your right hand, your choice of nodes is restricted somewhat because the location of your right hand is dictated by comfort and desired tone, and you must pick nodes which coincide with these factors.
Nodes to Notes
Here are the four strongest harmonics found on any string, named after the location of their nodes.
12th fret - sounds as an octave of the open string, same pitch as the fret itself.
7th fret - sounds as the perfect 5th of the open string, and octave above the fret itself (same pitch as the 17th fret).
5th fret - sounds two octaves above the open string, same as the 24th fret.
4th fret (actually very slightly behind the 4th fret) - sounds as the major 3rd of the open string, two octaves above the fret.
So in total we have: Octave, 5th, Octave, major 3rd. This gives us a major triad on each string.
As I said, these ratios are the same for Artificial harmonics. If you use your left hand to press down at the 3rd fret, move all the harmonics positions up 3 frets.
As for application of harmonics, here are a few chords to play around with.
E minor7
1. Harmonic: 5th fret G string
2. Harmonic: 5th fret D string
Open E String
The open E is your root. The first harmonic gives you the note G, two octaves about the open G string. This is the minor 3rd of the chord. The second harmonic gives you the note D, two octaves above the open D string. This is the minor 7th of the chord.
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G major
1. Harmonic: 4th fret G string
2. Harmonic: 5th fret D string
3rd fret E string (G)
The low G is your root. The first harmonic gives you the major 3rd of the G string; a B. This is the major 3rd of the chord. The second harmonic gives you the second octave of the open D string. This is the perfect 5th of the chord.
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C major9
1. Harmonic: 4th fret G string
2. Harmonic: 5th fret D string
3rd fret A string (C)
The low C is your root. The first harmonic gives you the major 3rd of the G string; a B. This is the major 7th of the chord. The second harmonic gives you the major third of the D string; F#. This is the 9th of the chord.
I hope this is of some use in getting you started with harmonics. Feel free to PM me if you have any questions about anything. | 
