Those are the guidelines

As stated those are the guidelines.  You must practice and continue to shoot in order to become better at utilizing these components.  I studied in college and put in my time, now the rules are second nature and only occasionally do I find myself going through each step before I shoot.  I simply approach a scene look at it and then I compose the picture.

When you're first starting out use a tripod and go through each step one at a time, they're your checklist for the picture.

1.  Horizontal or Vertical?
2.  Rule of Thirds?
3.  Balance?
4.  Repetition of Form?
5.  Leading Line?

Your pictures may not all have these fundamentals, and that is ok.  Not every composition will lend itself to these concepts but by implementing just a few or trying, you will get better at photography, your pictures will get better, and you'll become more appreciative or your own pictures and the ones floating around you.

Practice, Practice, Practice

Horizontal or Vertical

The first thing you must decided before taking a picture is Horizontal or Vertical.  There are many ammeter pictures I see that could be better if the photographer had simply chosen to shoot vertical instead of horizontal, or vice versa.  Skyscrapers, if shot from the ground, create a vertically strong theme and therefore the image should be composed as a vertical.  Boats and cars and items that are longer than they are tall should be composed as a horizontal.

Balance

Balance is the way subjects and/or items are arranged within a picture.  Many people shoot portraits with landscape and such in the background.  Often times they'll place the subject(s) off to one side of the picture so that the landscape can be viewed with little or no obstruction.  This is good practice but moving the people too far left or right of center can throw the picture off balance.  My own translation of balance is, "How the visual weight of the items (people, trees, cars, etc), in a picture, are distributed."

Leading Line

Leading line is a concept that uses the idea of lines to lead the viewers eye throughout the image.  Lines don't need to be so obvious as an a physical line it can be a perceived line.  A perceived line can be created by several objects in a row or aligned in the same direction or shape.  For example 7 flower pots forming an 'S' shape in an image with a subject at the beginning middle and end.  Leading isn't a necessity for all images but many times it can make any image better.


Note the strength of the beams (and their repetition), and how they push your eye up into the picture.  Leading line can be used in many ways, this is a simple example.

Repetition of Form.

This is really a pretty simple concept. Simply put it the use of the same or similarly shaped objects in a photograph.  Imagine an apple picking basket filled with apples.  That is repetition of form.  There are countless ways to include this technique into just about any photograph.  It can be the center of attention or simply an element within the image, it's your choice.  I've read many photography books and none of them ever had pictures to show the 5 fundamentals of composition.



This is a great example for repetition of form.  Looking at the box there are three primary repetitions.  the vertical strips of sunlight, the vertical strips of wood, and finally the vertical shadows.  There are more but those are the primary ones.  Also, note the leading line created by the drag mark, it also creates movement.

The Rule of Thirds

The rule of thirds is typically one of the hardest concepts to understand, in painting & drawing a similar concept is called the golden triangle..  That being said many cameras and phones automatically overlay a grid or have the ability to overlay a tic tac toe grid.  This is the basic idea behind the rule of thirds, and although there are infinite possibilities for the application of this concept the idea remains the same.  The way I've always thought of it is the visual break up of the image.  For instance a sunset picture might have the horizon line at the top third of the picture while the water meets the sand near the bottom third of the picture.  Aside from Horizontal or vertical the most important element in composition is using the rule of thirds.

I chose this example because of the light and dark areas of the photo.  The dark area on the right takes up about 1/3 of the entire space of the image while the lighted area takes up the other 2/3's.  This concept is not about mathematics so much as it's about visually distributing subject matter in a balanced and smooth fashion.  It's a concept that can be shown several different ways.