Photographic Composition is what seperates generic point-and-shoot photography from actual planned and thought out photography. Without knowing how to properly compose a picture, you may have a SR4,500 camera complete with accessories, but will still be taking bland pictures.
A camera is a tool, and no matter how simple or complex a tool is, the effectiveness of this tool relies on the operator. For an example, let's use one of the simplest tools, a hammer. This hammer has the full ability to drive a nail perfectly straight without bending it or smashing your fingers in the process, but if you don't know what you're doing, you can end up with a disfigured nail and a disfigured thumb to boot. That nice shiny camera may be excellent at reproducing your photograph on a digital or film medium, but you may not be using the camera properly, or 'hitting the nail on the head' so to speak.
The primary things to think about when composing a photograph are your subject, your surroundings, and your positioning. Before taking a picture, ask yourself, 'What do I want to accomplish with this photograph?'. Create a goal or objective, plan it out, then make that plan work. There are two basic ways to do this; position your subjects, or position yourself.
A good way to teach yourself composition is to read up on the subject, then study others photographs, asking yourself questions such as 'What was the subject in this picture?', 'Did the photographer do a good job of making the subject the primary and immediate point of interest?', 'If not, what could have been done to change that?', 'Is the background visually pleasing, are there any distractions?'. Of course there are tens of questions which you could ask, and these are just a select few, but reding this article will give you an idea of what to look for.
One good technique to get a feeling of what a scene would look like as an actual photograph is to make a frame out of your hands and view the scene through this frame. This effectively gives you a sense of border, and also blocks out items which may be otherwise distracting you from the actual scene at hand. Below is an example of this.
Viewing potential photographs through a 'hand frame' can give you a good feel for the end result.