This post is one of ten appearing in the series 10 Ways To Improve Your Landscape Photography. Composition concerns the placement of objects within the frame, and indeed the frame relative to the scene itself. It's a massive subject area that I just can't do justice to here. It really is worth spending time to study it - reading books on theory, viewing others' images and practicing.
For now it's worth considering a few things that will benefit your images if you aren't already making considered compositional choices.
Rule of thirds
Most photographers will have heard of this. Whilst it's quite common at the moment to berate its limitations and lack of creativity, if you are generally unfamiliar with the language of composition it serves as a useful starting point (though it should serve as no more than a guideline rather than a "rule").
The concept is to split an image into 9, basically by drawing a noughts and crosses (tic-tac-toe) board on top of the image. The intention is then to place key elements on one of the crosses where the lines intersect. If it's an object that takes up the height or width of the image, such as a tree or the horizon, you would place it along one of the lines.
The principle is that by using the lines along the third you create more tension and drama in the image than placing the subject in the middle of the image otherwise would to make it more engaging for the viewer.
It's common for beginning photographers to see a scene that moves them and attempt to take it as they see it. The reality is that what our eyes see does not translate well into a photograph, and the sense of wonder at a large expansive landscape is often lost in the process of image creation leaving the viewer asking "so what?" The inclusion of an interesting foreground object such as a rock or a tree will help to create more depth and interest within the image.
Make sure that the object is prominent enough so that it doesn't look like a random inclusion. It's common to stand too far back and the effect of a wide angle lens can make the foreground object become small and look like clutter, so make sure to get close (within a foot to a yard or two depending on the object itself).
Our instinct is to include everything in the scene in front of us. However the result can lack focus and appear cluttered. To make a clearer, more cohesive image try to remove objects from the image that aren't important to your vision. There are various ways of doing that, perhaps using a longer focal length, changing position or a smaller aperture. The most important thing is to be intentional in what you include.
Avoid random tree branches, unwanted farm buildings, fence lines, telepgraph poles, ugly rocks, etc creeping into your frame if you can help it. Often we only see these at home when reviewing images so it's important to really consider what's in your frame whilst in the field.
The process of turning our 3D vision into a 2D image completely transforms a scene. Where we have a concept of depth and spatial separation, the camera only sees different tones. What can look to us as quite separate and distinct elements, the camera will turn them into indistinguishable clutter.
A common problem I face is I see a lovely lone tree that looks very stark to me, but in my photograph it merges into the grass and heather behind such that it is completely lost in a sea of similar tones. There are various ways to overcome this, and essentially it comes down to providing contrast - a tree against a blue sky won't get lost as the brown and the blue contrast with each other.
Leading lines and curves
We can use lines and curvers to give a path for our eyes follow on a journey through the image. Common leading lines would be a path, a fence or a river but there are so many that we just have to keep our eye out for them! We want them to direct the viewer to our subject or to lead us through the image. It's common to start a line running from a corner of the image running to or through the centre of the image.
Because the draw on the eye is so strong, we want to avoid lines that draw us out of the frame - a fence that runs in the opposite direction to our subject and off the side of the image is going to unbalance the image and lose the viewer's eye. It's important to either change position to better lead the eye, or remove it from the composition.