Cropping and editing
Since you can't move elements of the landscape around to suit your composition, you have to position yourself and frame your shot to make the compositional rules work. However don't be afraid to crop and edit your shots using photo editing software to improve the composition afterwards. The limitations of the aspect ratio of your camera's viewfinder or monitor screen aren't always ideal for every landscape shot, and you may also find it necessary to crop out unwanted elements intruding into the frame. Most modern digital cameras have resolution to spare, so it's possible to crop down to quite small areas of the frame and still get a printable picture.
If you have the skill and the patience, you can also move some smaller elements of the image around to improve the composition. For the real landscape purist cheating like this is tantamount to blasphemy, but in my opinion if it results in a better picture then it's worth it. Even a subtle change can have a dramatic effect on the overall picture. Take a look at this shot of a sunset over Bournemouth Pier.
Ten minutes with Photoshop and the result is a much nicer composition. I simply moved the seagull over to correspond with the rule of thirds.
Finally, remember that all of these composition ideas are just guidelines. Nothing is written in stone, and if the end result is a good picture that you are proud of then it really doesn't matter how you took it. Now go out and get snapping!