A very basic but effective "rule" to follow is the rule of thirds. It is sometimes referred to as the rule of ninths because of the nine squares that are present when the frame is divided.
Imagine your photo divided into 9 equal parts using 2 vertical lines and 2 horizontal lines like in the image below.

Placing the subject on any of the lines or intersections will produce images that are better balanced and more appealing to the eye.