Perhaps this is a good place for me to inject my background a bit. When I was in High School and College I was an art major. The book that put me to sleep every time I tried to read it was a very thick volume called "The Art Of Color and Design." I do not remember the author, I do know I never got through it.
I was taught that a good composition overlapped the objects in it, that your eye needed an entry point, a path to follow, (elements that attract the eye) balance between the elements in a picture and an exit point. These things are valid, but most photography courses and critics have a big problem with what they call mergers (the intersection of objects) which can lead to some confusion if you happen to be taking a picture of a group of anything.
Developing you eye for composition is important to creating pictures rather than just being a snap shooter. If your pictures lack some of the elements of design and composition, it should be because you are choosing to ignore them, not because you are unaware of them or do not know how to accomplish them.
So on to the basics of photographic compostion. Think of these not as rules but as guidelines that you will sometimes want to sacrifice but do so knowingly and with intent.
Simplicity (yes you will hear this one over and over again)
Fill the Frame (again, repetition of this idea)
Consider Verticals
Find the Lines
The Rule of Thirds (I briefly mentioned this before )
Balance
Framing (not to be confused with filling the frame)
Avoiding mergers
Simplify: When you are thinking about simplifying, you need to have in your mind what you are trying to say with your picture. What is my message with this photo? What is the best way to communnicat this message?
Anything that is essential to the message must be included. Things that add to the message can be included. Anything that distracts from the message needs to be left out.
Fill the Frame: This does not mean that you need have your subject touching every side of the frame. What it means is that your main subject should be largest and most prominant in the picture. Extranious space should be done away with.
Lets say you are doing a portrait. If you hold your camera horizontally, you will have excess space either on one or both sides of your subject.
Another way to look at it is, a painter would not leave part of their canvas totally blank. Think of your viewfinder as a canvas and make the best use of the whole canvas.
Note here that while most pictures you take will be rectangular, there is absolutely nothing wrong with a square picture. This of course can be accomplished in the editing process.
Your subject will be strengthened by being closer or larger in the frame, and weakened by being too small or too far away.
Consider Verticals : Portraits generally are a good example of when vertical composition is prefered but that is not the only time to consider them. Even landscapes can have very strong vertical elements to them. Trees, mountains, waterfalls, buildings, uprights of bridges can all be very strong vertical elements. Depending on your perspective, even horizontal things can be vertical elements. An example is standing in the middle of a bridge looking up the river, the river can appear to be a vertical line.
Find the Lines: Just about anywhere you point your camera you can find lines. Use the lines to enhance your photo. Consider diagonal lines, leading lines and curved lines.
Diagonal lines are much more dramatic and dynamic than horizontal or vertical lines in most cases. This is frequently a matter of perspective in nature or landscapes.
A leading line may extend from near any of the four corners of a photo toward the middle of the image or toward a significant feature in the image and is one that your eye follows, and can be very effective in bringing attention to your subject. It can be the border of a field, a riverbank or a line of trees in nature. They add depth to your pictures.
Curved lines add aesthetic appeal such as a curve of a railroad track or river which also can give your composition depth. There are s-curves like clouds, winding rivers, vines, snakes gnarled trees and more that can all appear beautiful to the eye.
The Rule of Thirds : Before you snap the picture, imagine your picture area divided into thirds both horizontally and vertically.
The intersections of these imaginary lines suggest four options for placing the center of interest for good composition.
Which one should you use? That reallly depends on the subject and how you want the subject to appear. Generally you want moving objects to appear to be moving into the frame rather than out of it. That leaves only the top or bottom third ot consider. Does the subject cast a shadow? If the shadow mimics the shape of the subject it can add to the balance of the overall composition. Perhaps there are footprints in sand or something else that creates a sense of balance or shape repetition which can enhance your photo.
Balance: Getting good balance in your photo requires combining colors, shapes and areas of light and dark that compliment each other. Think about your subject and capture it from an angle, view or time of day that compliments your subject and draws attention to it or gives it that drama you want to convey. It actually is easier to do than to explain, and with some thought and practice you will find this starts to make more sense.
Framing: What I am refering to here is using elements of your photograph to frame the subject. A low close in tree branch and trunk creates a frame for the barn in the field, or the archway of the overpass can be an interesting frame for the church spire. The spokes of a wagon wheel or bicycle wheel can frame a variety of things from the face of a child to a couple on a blanket having a picnic.
Since this is a device to draw the viewers eye to a specific place it is best not to overuse it.
Avoiding Mergers: Avoiding mergers does not mean you must have space between all objects in your picture. A group portrait is far better composed if there is not space between them. The mergers to be avoided are things like a tree in the background appearing to grow out of someone’s head.
There is another kind of merger to be avoided, and that is a border merger. That is to say, when you crop out the feet of someone or the wing or tail of a bird, you have a border merger. This tends to anchor the subject to the edge of the frame which kills any action that might have been implied.
Close mergers may not be as objectionable, but can detract from the subject. When composing make sure that tree in the background is not going to take away or distract. (this also goes for the beach umbrella, the boat, the whatever) If there is something that appears to be going to create this merger or near merger, try changing the angle at which you are shooting. Try from a lower angle, or slightly to the left or right to fix this defect in your otherwise good composition.