Basically, if you imagine a photo divided into thirds, both horizontally and vertically, the main subject of the image should be where a vertical line cross a horizontal one.
Many modern cameras allow you to place a grid in the viewfinder which can be used to place the object where two lines intersect. While we are talking about the Rule of Thirds, it is generally best to place the horizon on one of the thirds, rather than in the centre of the frame, dependent on whether the main points of interest are in the sky or on the ground.
These lead the viewers eyes into the picture either to the main subject or on a journey through the whole of the picture. Examples of leading lines could be a path wandering through the image, a fence line, a meandering road or a stream or river.
To demonstrate that the rules are no more than guidelines, the next one contradicts the Rule of Thirds. If your image is symmetrical, then it could benefit from being centred either on the horizontal, or vertical centre line. This works particularly well for reflections
Rule of Space
This rule is talking about giving the subject in the photo, space to move into the frame. This particularly applies to animals and vehicles. The object should have the most space in front of it, and not be right up to the edge of frame, giving it nowhere to go.
Rule of Odds
Generally speaking, it is thought that photos with an odd number of subjects is more visually appealing and natural looking than those with an even number, where the viewers eyes may flick around the image, unsure of where to settle. I tend to use the rule of odds particularly if taking a close up of flowers or the like.
I hope that I have given you a brief insight into composition and that when you next look through your viewfinder you will at least stop and think for a few seconds at what you are looking at and how the shot may be improved. But just remember, these rules, and all the others you will come across, are simply guide lines to help you go in the right direction, they are not railway tracks that you have to stick to rigidly. Finally I will end with the words of Pablo Picasso – “Learn the rules like a pro, so you can break them like an artist.”