My photography teacher keep harping on 'composition, composition, composition!" He says a good photographer knows it when he sees it. I must not be a good photographer because hekeps rejecting my work - he says my compsition is weak.
Entire books have been written on this subject. You can start with the "rule of thirds" where the main subject is near the intersection of two line one third across and vertical on the page.
I would suggest to post a photo or two here and ask for an honest critique of composition. Don't be thin skinned. The folks here will be glad to offer good and bad (but honest) and suggest ways to improve. I found this is best way to improve my photos.
Composition is mostly about balance and emphasis. It takes practice and it's usually a continual process for most of us. Once you get the rules down then you can learn to break them. Here's an example of breaking all the rules but it's a shot that people like. However when in doubt go with rule of thirds and "fill the frame with your subject." I have done none of those things, but on purpose so it's ok
Solstar wrote: Composition is mostly about balance and emphasis. It takes practice and it's usually a continual process for most of us. Once you get the rules down then you can learn to break them. Here's an example of breaking all the rules but it's a shot that people like. However when in doubt go with rule of thirds and "fill the frame with your subject." I have done none of those things, but on purpose so it's ok
Browse through well known photographers galleries on the web to get an idea of what good compositions look like.
For landscapes, try...
Galen Rowell, Peter Lik, David Meunch, Art Wolfe, David Middleton, William Neil, John Shaw, Dewitt Jones and Ansel Adams to name a few. These guys are all compositional masters.
Maybe some folks here can name a few others who shoot other subjects than landscapes....?
A combination of curves and straight lines makes an interesting image. In a landscape, look for isolated or unexpected subjects such as a tree silhouetted against a plain background or a tricycle left in the middle of an empgy field. Look for something that leads the viewer's eye into the picture - a fence, a winding river or a road.
Isobell, look at the photo you're about to take and ask yourself this question. If I were looking at this in print, would I remember it 5 minutes after i walked away from it? An hour? A week? If the answer is "yes," especiall to the "week" self-question, then you probably have a photo with strong composition.
Don't be afraid tocrop after you take the photo. Sometimes the greatest shots are actually one cropped section of a larger view that just wasn't that spectacular. The photographer didn't see the isolated view until looking at the overall photo or print.
Some examples from my work though not the examples you will get with some of the sugessted shooters it will be a start for you
As was said check out the galleries here on PT especially Karl Wertanen and Fay Vincent and Crystal Wightman you will see good composition of landscapes. I post mostly sports so my galleries give you ideas on composition of sports shots. Keep practicing and you will get it better
Great posts here. Yes, the rule of thirds is a good generality when considering pleasing composition. You can balance a lot of landscapes with rule of thirds. You'll find horizons are especially important in landscapes, so pay extra attention to where the horizon is. Good composition will come with practice. With practice you'll be able to recognize what draws the eyes where, and how to notice and balance all the subjects within the photograph before taking the shot. If your instructor is telling you your composition is weak, ask him/her why, and get some critiques. Ask how that particular shot could be improved. Get input from your peers too.
What helped me really early on, is that right before I took my shot while my eye was in the viewer, I'd scan the frame from corner to corner, and asked myself, "is this shot a keeper? what am I trying to say with this shot. what's the emphasis in this frame?" I'd realize sometimes I'd have a cluttered background, badly composed horizon, things being cut-off on the frame corners, distracting elements, or just a downright boring composition.
A photographer does know it when they see it, but it is also highly subjective. I may compose a shot one way & it works, you may compose differently & it works, & a third person may look at both of our works & say he hates them both.
But before you can go breaking the rules, you need to learn what they are 1st (like the rule of thirds). The best way to refine your composition is with LOTS of practice & lots of exposure to work you like. Like Baydream said, there are many books available on the subject. Just don't get discouraged, it'll come in time.
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This is a GREAT photo Solstar! 
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