Some compositional rules of photography

BALANCE: What happens to eyes when they look around a photo?

Rule of Thirds

• The rule of thirds is a compositional rule of thumb in visual arts such as painting, photography and design that states that an image should be imagined as divided into nine equal parts by two equally-spaced horizontal lines and two equally-spaced vertical lines, and that important compositional elements should be placed along these lines or their intersections. Proponents of the technique claim that aligning a subject with these points creates more tension, energy and interest in the composition than simply centering the subject would.
  
  
• Photos are more effective when their focus isn't right in the center: it's too static and doesn't move the eye around it.
  
  
• When the focus is on the lines / A B C or D, it's more effective as it opens up the eye to exploration.
  
  
• Lines parallel to the frame break it up.
  
  
• Curved / diagonal lines are the most energetic.
  
  
• The most dominant element of balance is visual weight created by an even distribution of the emphasizing elements (sharpness, brightness, etc).
  
  
• Using the Rule of Thirds comes naturally to some photographers but for many of us takes a little time and practice for it to become second nature.
  
  
• In a similar way a good technique for landscape shots is to position horizons along one of the horizontal lines.

SIMPLICITY

• Get close
  
  
• Carefully select your subjects / think about how much of a figure or subject you need to include. Where does it crop? Why?
  
  
• Think about perspective
  
  
• Think about eye movement (shoot high / shoot low)

LINES

• The eye follows a line instinctively.
  
  
• Pointing to our subject? Framing our subject?
  
  
• Perspective refers to two converging lines.
  
  
• Lines can be real objects, or the product of shadows
  
  
• Horizontal lines give the viewer a feeling of calm, stability and weight.
  
  
• Vertical lines can express strength and power.
  
  
• Diagonal lines give a sense of movement within a photograph
  
  
• Curved lines draw the viewer's eye through the image in an orderly way.
  
  

SUBJECT OF EMPHASIS:

One of five factors determines what becomes the most important element of an image:

• The closest point to the viewer
  
  
• The brightest point
  
  
• The point of sharpest focus
  
  
• the point to which main lines converge
  
  
• Filling in the frame by contrast
  
  

DEPTH

• The dimension, mainly distance and volume in a photo, is represented mainly with a range of focus — out of focus effect.
  
  
• Walk the viewer through layers of differing distances.

LIGHT

• The black and white photographer's medium
  
  
• Direction of light: decides where shadows will fall and its source can be described by its relative position to the subject.
  
  
• Light can be high, low, to one side, in front of or behind the subject.
  
  
• Contrast: quality of light.
  
  
• Harsh light produces an image where the dark and light tones dominate over the mid-tones.
  
  
• Soft light: coming from a large source such as sunlight that has been diffused by clouds, or light reflected by a surface.
  
  
• Low contrast images are sometimes describes as "flat."
  

COMPETING ELEMENTS

• The closest point to the viewer
• The brightest point
• The point of sharpest focus
• The point to which main lines converge

Here's a nice article that goes into a little more detail.