Rule of Thirds is often quoted in composition. It says to divide
your frame into thirds both horizontally and vertically, and then place
your subject at one of the four intersections.
But, in looking for an image to illustrate this, I had a hard time finding
one that followed this rule exactly. I guess I am just a rebel ;->. I
usually place my subject off of center, using the horizontal or vertical
lines, but not necessarily the intersection points. Just keep in mind the
most pleasing placement is usually somewhere out of dead center.
This applies to where you place the horizon lines as well. Usually, right
smack in the middle of the frame is visually boring. Moving the line up or
down will dramatically improve the resulting image.