The Golden Ratio
Ever since its discovery the golden ratio has been subject of debate and pondering amongst both artists, philosophers and mathematicians. The golden rule of proportion seems to supply us with an almost perfect principle of balance in both a mechanical and aestethic sense. We will not deal with the technical and mathematical matters of the rule in this art tutorial but just for the sake of it we can describe it by the formula given below:
B/A is equal to A+B/B (same deal with B related to C)
Note: B and A (and C) represent lengths (see illustration below).
It's Everywhere
The golden ratio can be found in the construction of many buildings such as the great pyramids, in geometrical shapes, in music, fine art, various places in nature and even the human DNA seems to have been constructed with this rule in mind. It's quite a mystery really and if you feel like digging deeper into this enigmatic rule a link is provided at the end of this tutorial. But lets move on.
An Example
Take a look at the arm below divided into three parts; the upper arm, lower arm and the hand. Notice how the upper arm is a bit longer than the lower arm, and the lower arm is a bit longer than the stretched hand. Now, take a close look at the little finger of the hand. As you can see the three parts of the finger are divided in the same manner as the entire arm. The same rule also applies to the human head, the legs and many other parts of the human body.
Vitruvian Man Example
For the sake of another example I took the liberty to use Mr. da Vincis excellent Vitruvian Man and edited him a bit. I hope he doesn't roll over in his grave. Now, as you can see in the picture below the golden ratio applies to the entire body as well, where:

A = Head/Neck
B = Body
C = Legs
Vitruvian Man
Again, if we look at a single leg it would then be divided like this:

A = Thigh
B = Lower Leg
C = Stretched Foot

Please bear in mind that it is not absolutely necessary for you to understand all the mathematical details of the golden ratio. Just make sure you understand it well enough to use it to your own drawings and paintings.
How can I use it in my art?
The golden ratio is an excellent tool for getting the right proportions drawn. The only requirement is that you have this rule in the back of your mind when you draw or paint. And when you have it worked in real good you can even start bending the rules of proportion and get some interesting results.
Wait, there's more!
To get fully acquainted with the golden ratio I suggest you visit wikipedia and read the rule of the golden ratio article covering far more on this mysterious and universal rule.