Learning how to compose great shots is an art, not a science. There are many 'rules', which are certainly worth familiarising yourself with (which is why you're here), but successful photographers know when to follow the rules and when to break the rules. Often it is by choosing an unusual and unexpected composition that leads you to the most successful images.
An Introduction:
The Art of Composition:
Examples of different approaches to composition:
Camera Angles:
Creative Camera Height, Angle & Crop:
Square Crop:
The Art of Looking Down:
Additional Reading:
Michael Freeman
The Photographer's Eye
"…how you build a picture, what a picture consists of, how shapes are related to each other, how spaces are filled, how the whole thing must have a kind of unity.” (Paul Strand)
This book is intended to explore the actual process of taking photographs. Taking good photographs has more to do with how you compose your images and how you frame your shots, than the type of camera you buy, the lens you attach or the settings you use. Michael Freeman's book is a comprehensive guide to composition.