In this sample video from Martin Taylor's online guitar lessons we'll get into a topic that Martin also mentions in his guitar lesson about tuning: harmonics.  Martin talks in-depth here about playing harmonics and also covers sound waves, arpeggios, and how to combine natural and false harmonics.  

Harmonics come from basic physics by modifying sound waves.  Plucking a guitar string naturally oscillates at not one, but several frequencies (which are known as partials).  Since the guitar string is long and thin, many of the partials are multiples of the frequencies which are called harmonics.  These sounds made by long, thin oscillators are considered musically pleasing and are also fun to play.  So let’s get started! 

We'll begin on the twelfth fret where you can get a natural harmonic sound fairly easily.  Go above the fret and let go so you can hear the harmonic but also keep in mind that you can get natural harmonics in different areas of the guitar.  Keep in mind, we are just disturbing sound waves here.  You can mix harmonics starting from the 2nd string, 7th fret, first string and the 10th fret.  You can work your way down or up the fretboard and get a natural harmonic sound without pressing any strings down.

We can also do false harmonics by making the sound wave different.  A harmonic on the 12th fret is half-way.  If you press the F there will be a natural harmonic.  You can also use a pick to follow up with a left sharp and 12th fret to get a false harmonic.  All you do now is follow the pattern that you are playing 12 frets up.  Now you can make music out of this by combining natural and false harmonics, and also the natural notes.

Here's an example: try playing an open D string and then play the harmonic on the 6th string. Then move up to the third string open, fifth string harmonic, second string open, fourth string harmonic, first string open, and then third string harmonic.  You'll start to get nice arpeggios and a harp effect. 

You can experiment and play around with harmonics for ages.  Martin recommends that you check out Lenny Breau and Tommy Emmanuel who are masters at playing harmonics.  One word of advice is that you should use it kind of sparingly and not all the time...  Find a good spot to add harmonics so that you don't give away all your secrets at once.  When you are playing your solo it's a good idea to not go straight into playing harmonics but rather save it for the end or in a place where it will be effective by using it in a musical context.  That is how you can use it best.  Otherwise it can sound disjointed and will not have the same depth or meaning to express yourself.  

Have some fun finding your own different shapes and enjoy experiementing with these harmonics!