Landscape photography is very interesting, there are so many elements that can create different moods and feelings to an image, different light, different times of day and different effects of your pictures can totally change the feel of a location.
To create stunning landscapes, most landscape photographers use a wide angle lens, most entry and enthusiast DSLRs can be bought with a kit lens, often 18-55mm for Canon/Nikon or 14-42mm for Olympus, taking in to account that these range of cameras don't use a full frame sensor like pro models, you will be getting the equivalent of a 28mm lens at the widest setting. This is wide and you may find that this lens will produce results that you will be happy with, but to get the most out of landscape photography you might need to consider a wider angle lens such as a 10-20mm lens.
At the widest setting, this kind of lens starts to produce an effect called 'fisheye'. This can create very dramatic results, but the picture does look distorted - see example on left.
When taking a landscape, consider the mood you want to create, try shooting at dawn or sunset, try using slow shutter speeds on moving water to create a dreamy effect, or capture early morning mist over a still lake.
When composing a picture, consider the golden third rule applied to paintings, for example if taking a picture of a tree, don't have it in the centre of the shot, have the tree to the left or right. Although rules are made to be broken and often, striking results can be captured if you don't apply this technique.
If taking a picture of a sky, try and have some land at the bottom of the shot to give an idea of scale, this will make the sky look at more dramatic.
For a landscape shot, you will probably want everything in focus within the frame, from the blade of grass in the foreground to the mountains in the distance, to do this you will need a small aperture - high F stop number and focus somewhere in the midground, remember though that this will reduce the amount of light let in to your camera so a tripod will be needed to ensure a sharp shot.
Often, when taking a picture of a landscape you will notice that there is a great deal of contrast between land and sky, where most DSLR metering will do it's best to find a nice middle tone as to not over/under expose areas, you will often find that your sky is bleached out with no detail, or land is vastly under exposed (dark). To compensate this effect, landscape photographers use filters, a good filter to try is a graduated Neutral density filter, this filter is available in different strengths and will help diffuse the brightness of the sky so that your picture is more evenly exposed. See example on left. The ND filter is grey, but it's a neutral grey so whatever light it lets through isn't affected in colour, just in brightness. The ND filter is also useful if you want to slow down your shutter speed, for example you may want to blur a waterfall, by attaching an ND filter the brightness from the subject is dimmed, therefore your camera will select a slower speed, otherwise if you selected the shutter speed manually, the water would be bleached out to white because the shutter speed would be to slow for the conditions, therefore an over exposed image would result.
Another method that photographers use is something called HDR imaging. Using a tripod, you take a series of images from the exact same spot ranging from under exposed to over exposed. Your DSLR will have a feature called auto - bracketing which will do this for you. The images can then be overlayed together using photoshop or other graphics programs to achieve a well exposed image. Some of the results HDR offers is stunning.
The main thing is to get out there and practice, experiment with filters and HDR, unusual angles and different times of day.