Photography is about light and color, so the basic rule of photography composition is getting the most of both in each frame of the image. To get that extra edge you should know how to make the most of the limited light available to you by using depth of field. To make this work you have to use your focal point, which is the center of the scene, to dominate the entire frame. Remember, a camera sees everything from just one meter away so focus is everything. Remember the rule of thirds and you'll be fine.
Your first rule of photography is that objects with clear focus are the main subject of the frame. Forget everything else, your background, anyone's clothes, trees, and the sky. Simply put the focus of the frame on your subject. This means you need to be very precise with your composition. A single point can mean anything, a bird in the foreground, a street scene or even a distant tree. In most cases it's the center of the frame.
The second rule of composition technique is the use of the thirds. This is a common enough photography tip that most people know it already. However, in photographs where the main subject is a form of art, this rule literally comes in handy. If you're photographing a landscape then you can use the thirds to show the listener the border of the scene.
The third rule of composition is as simple as it goes: get the eye in the shot. When you look through your viewfinder, always look towards the center. Don't look to the sides or towards the horizon. This will result in your camera lens not focusing correctly and therefore your photos will lack depth. With the lens wide open, it is impossible to achieve this effect so try to focus on the depth of field around the focal point instead.
The fourth rule of photography is the use of the straight sides. This is an easy one and should go without saying. Almost every single photograph that you take needs to have a strong sense of direction and using the straight sides can make this happen. When you draw the horizon line to indicate the limits of your frame, your viewers will be able to see exactly where you are in the photo and your photo will have more depth.
These are the four photography composition rules that should form the foundation for your work. As long as these four elements all play off of each other then your picture should follow the natural flow of the image's light and depth. You should never be concerned with how other people will see your work because as long as you're taking photos within the guidelines laid out here then they won't be affected in any way. In the end, you want your image to speak for itself so to keep everything simple and your pictures will speak for themselves.