Artificial harmonics are good because you can produce a harmonic on any note, rather than just E, A, D, G and B. In order to understand them, you will need a basic understanding of natural harmonics.

You produce an artificial harmonic by frretting a note and placing your thumb over a specific fret bar as you pick. The fret bar where you put your thumb is determined by adding on the fret number of a natural harmonic onto the fret number which you are fretting. For example, you can find a strong natural harmonic at the 12th fret. This means that if you are fretting the 3rd fret, you add 12 onto 3 to find the spot where you place your thumb. 12+3=15, so you would fret the 3rd fret and as you pick, touch the string with the part of your thumb which is nearest to the string over the 15th fret bar. Once you have picked the string, take your thumb off of the string to let the harmonic ring out. This will produce a sound which sounds like a natural harmonic, except it will be fretted, unlike a natural harmonic.

If you are not using a pick, it can be a lot easier than this. Instead of putting your thumb over the nodal point, put your index finger over the specific fret bar and pick with your thumb.