Composing a photograph is based on perception: we perceive things to be arranged and designed. The Gestalt school of Psychology, which broadly speaking believes that humans see in terms of patterns, put forth the laws of perception to explain how we see things. It is the most important theoretical aspect of composition in my opinion.
[highlight]The law of Similarity[/highlight]
Simply stated, the law of similarity states that items that are similar are grouped together. Here's an illustration:
In the Illustration above, we perceive that the triangles are grouped together and the circles to be together. We perceive similarity when objects share the same shape, color, texture, size or brightness. Since we are dealing with photography, similarity can consist of similar facial expressions or body posture. Here's another Illustration:
Even tough the elements above are the same shape, they are not perceived to all be in the same group: Those who are lighter are grouped together and those who are darker are grouped together.
[highlight] How to use the law of Similarity in Photography[/highlight]
Knowing that what looks similar are grouped together, you can use it when taking pictures. Here's an example:
Here's how the brain essentially perceives the scene:
All of the Oranges and Yellows get grouped together, the cool colors (left area and man's arm on right) are also grouped together. So this photograph predominantly uses the similarities in color. Here's one photograph that also uses similarity:
What's similar here is of course the shadows. But there is also similarity in the posture and also the heads. The head is essentially an oval and is interpreted as such, the body is essentially a large stick and interpreted as such:
Since the shadows , posture and head are of similar shapes, they are grouped together, creating an implied triangle. Taking pictures of similar elements is usually enough, the relationship of the similar elements is crucial. The movement that the yellow-orange colors make from the color photo above lead your eye from left to right. For the photo of the people walking, I waited until I saw a triangle was formed. Without that triangle, the photo wouldn't be as successful compositionally:
Notice how the similarity is there, but it's not as strong as the previous photo. Here's one last example:
I liked the way the bars came right at you when I held up the camera. I waited and waited until three people walked in. Not only they all have a similar posture, their distance from each other made it possible to create a similar triangle than the one on the left. There's much more going on in the picture, but here is the main similarity:
When looking at a scene, look for similarities in color, posture, shape, etc. Afterwards look at what relationship you can create out of the similarities. Things do not need to be clones of each other, a vague similarity can do, like similar body postures, etc.