Rule of 3rds is the rule that says to put the main object of attention at one of the thirds (not in the center) of the photo frame.
Leading lines says to include lines that lead the eye around the composition to generate interest.
Simple background says to keep the background behind the subject simple and free of clutter.
Leave room for motion says to keep a moving object off to one side and leave room in the photo for it to "move" into.
Complementary colors says to use colors that are opposite from each other on the color wheel such as red and green for a dramatic effect.
