All of the technical skills in the world can't give you an "eye" for photography. But, by paying attention to using composition in photography, you can improve your photos dramatically and produce more professional-looking work.
Here are my tips for improving your composition skills.
Learn "The Rule of Thirds." This age-old rule states that an ideal landscape photograph should be divided into thirds. You should start off by trying to have a third of the photo showing sky, a third showing horizon, and a third showing foreground. This leads to images that are aesthetically pleasing to the human eye, as we tend to look for lines and patterns in images.
Breaking the rule. Next, you need to learn when to break "The Rule of Thirds." (I never said photography was logical!) If you're photographing a spectacular sunrise or sunset, then you may want to include more sky than horizon and foreground (which are likely to be in shadow). If you're unsure, then experiment. You'll soon see what works for you.
Look for lines and visual points of interest. The human eye likes to be led into an image, and we automatically look for strong lines. Don't automatically place an object in the center of your landscape. The human eye looks from left to right, so try placing your object on the left-hand side of your photograph to lead the viewer into the shot.
Don't just shoot from eye level. This tip applies to both landscapes and portraits. Vary your point of view. Try kneeling or standing on something to gain a different perspective. You'll often end up with a more interesting shot this way.
Zoom in! With both landscapes and people, there is a tendency with those starting out in photography to try to cram everything into one shot. But, by picking out one area, you can achieve a much stronger image.
Use depth of field. In conjunction with the above point, learn to use your depth of field (by altering your aperture) effectively. A landscape needs a large depth of field (around f16/22) so that everything is in focus. But, if you're zooming in and trying to pick out an individual object or person in a busy scene, then a smaller depth of field can make the difference between a snapshot and a professional standard shot. By blurring the background, your chosen subject will really stand out.
Use the foreground. Remember that a strong visual point of interest in the foreground always stands out in a photograph. Try to place objects or people within the foreground of your frame.
Experiment with angles. When photographing people, don't just shoot them straight on! Most people have a stronger side to their face, so try experimenting with different angles. Have the people you're photographing tilt their heads, and remember to vary your point of view, as mentioned above.
Watch the eyes. Finally, don't fixate on eye contact in portraits. Sometimes you can create a very strong portrait if your subject is looking elsewhere. This can work particularly well in street photography, as it allows the viewer to imagine what the subject is looking at, and therefore draws them into the photograph.