Paying closer attention to composition is without a doubt the easiest way to improve your photos. For our discussion, I will break composition down into two categories: macro and micro.
First, let's consider composition at the macro level. You can think of this as the overall picture. Composition principles for photographs work the same was as they do for paintings.
A staple of fine art philosphy is the "rule of three." As you're looking through the viewfinder and trying to frame your scene, mentally disect the horizontal into three sections and the vertical into three sections. By keeping these nine sections in mind, you will avoid the calling card of the novice photographer: the dreaded bullseye.
The bullseye principle is simple. The dart, or focal point of a photograph, lines up dead in the center. Why is this so bad? Think about a portrait. If we position the face right in the middle, almost half of the frame is taken up by dead space above the head. You don't want to look at the air above your subject (unless you plan for a specific backdrop).
Wouldn't you rather see what the person is wearing or what position their body is in? Instead, frame the subjects face along the horizontal line separating the top two sections. (back to the top)
After paying attention to the overall framing, look a little closer at the details. What's the background made of? Is your subject standing in front of a fence, giving the impression a pipe is growing out their side? Is your background clean or busy?
For example, shooting with a brick wall as the background would make the picture look too busy, along with drawing the eye away from the focal point.
In the picture above, notice that there isn't a lot of clutter with other players drawing your eye away from the action. Sometimes moving yourself a foot this way or crouching a bit can make all the difference. (back to the top)