I'm not pretending to be an authority on how to do this, but here are my thoughts, anyway.
In brief, what makes a great landscape photo -- regardless of where it's taken -- is the photographer and his/her eye for the composition. That is a matter of training, intuition and taste, at the very least.
Judging from what I've seen of other people's photographs, I'd say that recognizing the following factors has something to say in finding the extraordinary in the ordinary:
- The rule of thirds
- Geometry -- shapes, curves etc.
- Contrasts -- light and shadow, or things that just don't match
- Texture and patterns -- fractals, similarities, reflections, ...
- Planning
Colours may or may not play a part in all of these.
When I mention "planning", it's not necessarily about planning exactly how a shot should come out -- by all means, do just that, it can give excellent results -- but it could also mean making sure that you get to the right place, at the right time, under the right conditions. From one vantage point, you might be able to visualize how it looks from another. Perhaps you're familiar with the landscape, knowing that at certain times of year, there will be a mystical fog around the forest floor, or the pools of water in a swamp catch the light in a particular way. Landscape photographers often talk about the hours when the light is right, which is usually around sunrise or sunset, but can also match the conditions on an partially or fully overcast day. It is not without reason; shadows and contrasts become more pleasing and also easier to capture within the dynamic range of film or digital.
Without making any claims as to the extraordinary nature or whatever in my own photos, I'll try to use them as examples anyway; they're taken in quite ordinary locations (sorry for the overt copyright notices).
Sometimes, you have to look away from the large, sweeping landscape views ...
... because they don't always work, no matter how impressive they look to your eye when you stand there; they're "postcard" shots. You could try looking to the closer, smaller things. Perhaps it's just a tree stub ...
... or something else that can catch your eye. Expect to do some cropping (for instance, to get rid of that annoying green patch in the upper left of the tree stub image) or other adjustments to give the image its proper "oomph".
I think the following photograph illustrates something about curves (connect the dots), contrasts between light and shadow, and how the rule of thirds can be used to place objects of interest so that they stand out in the frame:
This one was planned, but wasn't taken when the light was supposedly right (it was around midnight), but you can often make the light right by controlling your exposure. So this is a 1/5 second exposure at f/10 and ISO 1600. The reflected light you see comes from a summer sky, but of course it wasn't quite this bright to the eye.