I think of photographic composition as a secret knowledge - almost subversive, a "them and us" kind of thing.
Most people looking at photographs believe they are being emotionally moved only by the subject matter of the picture, and to a large degree they are: they are made sad by a picture of starving children, or joyful by a picture of a snowball fight, for example.
But they are unaware that the composition of the photograph also has a powerful influence on how they interpret the picture.
The photographer can exercise an almost subliminal influence over the viewer, who is getting a message but doesn't know how the photographer is delivering it.
The ability to compose your pictures well will empower you to take pictures that capture how you feel about a subject and to pass that feeling on to the viewer.
Here are the laws of composition: number one, rules are made to be broken! I don't like to be bound by laws, nor do I wish you to be, but there are some basic compositional pointers that you would do well to adhere to.
Even if you ultimately decide you want to go with your own ideas, please give these a try first:

1. The law of thirds: show that there are four key points in your frame, one of which should contain your picture's most important feature.
   
2. The golden triangle law: often used in portraits, urge you to create an equilateral - triangle shape within your frame.
   
3. Positive and Negative: You should aim to include important shapes between the subjects of your composition just as much as you aim to create good shapes with the subjects.
   
4. You can learn a great deal about composition by trying to copy some of your favorite artists' photographs or paintings.
   
5. There are many visual effects you can utilize to make your pictures more informative, appealing, or just plain weird.
   These include using symmetry, a second frame, and scale.