I second Poore's work, "Composition in Art" is a composition primer, available cheaply from Dover pubs. Sometimes I find the explanations rather obscure, but his book gives you the ability to analyze composition. He doesn't really take the "composition rules" road, rather he shows you how painters organize their work according to ideas like balance, line, color, shadow/light, etc. Once you can analyze a scene according to such tools (or similar ones, every artist have their own way of decomposing a scene), then you have a much stronger power in your hand.

Once you pored through Poore, go pick up a few painting books and a few photography books and try to see if you can reverse-engineer the way in which they are composed. You will be surprised to find geometrical regularities, equal areas of shadows and light, and so on.

The epiphanic moment about composition for me was when I realized that the pictorial space and the picture plane can be understood distinctively, so that you can build relationships between the two. For example, a vague shadow pattern that is happening in depth in a photo (3D), actually creates a perfectly geometrical manner on the picture plane (2D).

For me, it happened when I looked at the Polaroids series of Walker Evans. I was able to "get" seemingly banal pictures by understanding their composition. Eggleston does that to me too.