I'll probably admit right up front, this blog post might not clear things up for you. But if it gets you thinking, it'll be a step in the right direction.
I know many people want to take the cavalier attitude that "there are no rules…" or "there's no such thing as a bad picture." While there might be some truth to that, often those people fall into one of two categories. A.) They're lousy photographers B.) They don't understand composition so try to discount its importance.
There… someone had to say it.
Of course there are rules. Do they work? Yes. Are they hard and fast? No. Are they meant to be broken? Sometimes.
Rules provide a foundation for building. It's not much different than writing or any other form of communication. After all, your picture is or should be telling a story. So it's nice to have structure.
As far as rules being hard and fast, this is where you take artistic license. But know the rules before you break them. And I'm not sure "break" is the right description. Bend might be a better term.
A simple starting point is to view the scene and identify the elements that will best tell the story you want to tell. Keep the premise of telling a story as your goal. Overlay a mental grid to the scene. Along the lines of "the rule of thirds," use the grid to organize and bring balance or symmetry (that includes asymmetry) to how you'll use the frame.
Mentally walking around those elements, see how you can arrange them to make the story interesting and to give the viewer information that enhances the story. Check the foreground… background. And when I say "walk around," think three dimensional. So not just a circle, but a sphere. No just a rectangle, but a cube. Over, under, sideways down. (60's Yardbirds reference for those in the know.)
Three dimensional can be and often is important. We want to give the photo depth so our viewer can travel into the image. We can lead the viewer's eye providing a sequence to their discovery of objects within the story. A simple example would be when shooting children… get on your knees. Shoot at their level and put your viewer in the world of children.
The technical aspects of photography are also going to contribute to your composition. The time of day might be important. The direction of the light can also bring additional hints for the viewer. Is it morning? Is it night? Or does it even matter?
Of course in my field, motorsports, the pan shot, where the subject is followed and a slow shutter speed is used, is tremendously important. Sure, there's the simple technique of a side pan… but there are many subtle applications where camera movement and shutter drag is applied to capture the energy of the subject.
Lastly, don't forget the depth-of-field. Like the shutter speed in a pan shot, being specific and determined in your aperture selection can draw your viewers attention to the important elements of your image while blurring out less important or distracting elements.
Good composition can make or break an image. It certainly can change the viewers perception of the story you are trying to convey. We're not trying to make everything the same. But we are trying to make our image more interesting.
Look… all music is made up of the same scales of musical notes. There are lots of forms of music. But it is structured. Listen to the Doors play Light My Fire then listen to Jose Feliciano perform Light My Fire. Both good… but each uniquely different performances but still primarily the same notes. Regardless, both have structure.
Think about it.