If your shot is in danger of losing impact due to a busy background, crop in tight around your main point of focus, eliminating the background so all attention falls on your main subject. This works best with portraits as can be seen below.
The most basic rule of photography is the rule of thirds. This is all about dividing your photo into 9 equal sections by a combination of both vertical and horizontal lines. With the imaginary frame in place, you should place the most important element(s) in your shot on one of the lines or where the lines meet. This technique works very well for landscapes as you can position the horizon on one of the horizontal lines that sit in the lower and upper part of the photograph while your vertical subjects can be placed on one of the two vertical lines.
Our eyes are unconsciously drawn along lines in images so by thinking about how, where and why you place lines in your images will change the way your audience view it. A road, for example, starting at one end of the shot and winding its way to the far end will pull the eye through the scene. You can position various focal points along your line or just have one main area focus at the end of your line that the eye will settle on. By doing so you create balance in your shot as well as subtly guiding the eye.
Filling your frame with a pattern that repeats gives the shot more impact, exaggerating the size/number of the objects you're photographing. Shots, where there's symmetry in them such as lamp posts lining either side of a street, a long line of trees or a series of arches, can also be used to guide the eye to a single point. Just remember you need a focus point at the end of your shot otherwise it won't work as well. Symmetry can also involve non-related objects that resemble each other in shape, colour or texture. To be different, break the repetitive pattern with one shape/colour that stands out from the rest. You'll probably have to play around to see how positioning the 'odd one out' changes the composition/feeling of your shot.
Having fore-, middle- and background detail will add depth to your image as well as draw the eye through the picture. Compositional elements that compliment each other, for example with colour or by association, work well but do be careful with the size of objects you use and how you place them as you don't want the shot to be thrown off balance. You don't want a massive rock in the foreground of your landscape shot, for example, drawing the eye away from the hills and mountains in the background. Adding water to the foreground can also lighten your shot as well as adding an extra element of interest as it reflects the sky back out.
Frames have various uses when it comes to composition. They can isolate your subject, drawing the eye directly to it, they can hide unwanted items behind it, give an image depth and help create context. Your frame can be man-made (bridges, arches and fences), natural (tree branches, tree trunks) or even human (arms clasped around a face).