Rule of Thirds
The Rule of Thirds is based on the fact that the human eye is naturally drawn to a point about two-thirds up a page. Crop your photo so that the main subjects are located around one of the intersection points rather than in the center of the image.
Golden Section rule
It has been found that certain points in a picture's composition automatically attract the viewer's attention. Similarly, many natural or man-made objects and scenes with certain proportions (whether by chance or by design) automatically please us. Leonardo da Vinci investigated the principle that underlies our notions of beauty and harmony and called it the Golden Section. Long before Leonardo, however, Babylonian, Egyptian, and ancient Greek masters also applied the Golden Section proportion in architecture and art.
To get a clearer sense of these special "Golden" composition points, imagine a picture divided into nine unequal parts with four lines. Each line is drawn so that the width of the resulting small part of the image relates to that of the big part exactly as the width of the whole image relates to the width of the big part. Points where the lines intersect are the "golden" points of the picture
One side of the picture is divided into two, and then each half is divided into three parts. The adjacent side is divided so that the lines connecting the resulting points form a diagonal frame. According to the Diagonal Rule, important elements of the picture should be placed along these diagonals
10.Techniques of Photography
from notes during p4 infocomm club cca