I think the answer can be found in the study of Ansel Adams, unquestionably one of the greatest, most famous, and most popular photographers of nature. Not only was Adams a great photographer and writer, this question is one of the essential parts of his life's work: the legitimization of photography as an expressive art form, not merely a mechanical recording medium.
From a 1984 interview:
I think of Stieglitz's definition of photography — a paraphrase of what I heard him say many times. In the earlier days, when people were very scornful of what he called "creative photography" or "photography as art," they would ask: "Mr. Stieglitz, how do you go about making the creative photograph?" He would answer, "When I have a desire to photograph, I go out in the world with my camera. I come across something that excites me emotionally and aesthetically. I'm creatively excited. I see the picture in my mind's eye and I make the exposure and I give you the print as the equivalent of what I saw and felt." The word "equivalent" is very important. It's two things — what is seen and what is felt about it. That's why the naturalistic element in photography is very important. When you intentionally depart from the natural situation you can get into trouble. Unless you depart far enough.
(A video of a similar interview from around the same time is available on youtube. Skip the first minute to get right to Adams directly.)
Adams' "zone system" is a technique for exposure, but it's also a technique for taking the scene before you and producing a final print which shows these two elements, the seen and the felt; both, as you say, "the scene which was there", and an artistic interpretation of the emotional impact of that scene.
Your comment that "To me it sounds as if the scene was there and [the photographer]" reminds me of an oft-repeated but apocryphal Adams quote: "Sometimes I do get to places just when God's ready to have somebody click the shutter." But even then, one has to have the technical skills — the craft — to make that click happen just right. More often, taking a successful a landscape or nature photograph requires more initial effort than the final result may indicate. For some people, in fact, getting that feel of an effortless capture of natural beauty is a goal, even when it actually took a great deal of work to get into the exact right place at the right time.
So, this isn't a literal how-to answer, but I hope it points in the right direction to a larger, more comprehensive answer. I think that by carefully observing the work of some of the great nature photographers, and by reading what they have written, you can set yourself on the path where you can find the answer. Adams has a trilogy of books, The Camera, The Negative, and The Print which in this digital age can be seen as partially obsolete in a technical sense, but which are full of wisdom on photography in a timeless way. (And they're an easy, conversational read — and you can skim the parts that you don't find helpful or interesting.)
To distill what I can, though:
- Understand the process of turning a visual idea into a final image, from camera to post-processing to print (or online display).
- Find something that appeals to you emotionally or aesthetically — have something to say, even if it is just "these are pretty flowers".
- Visualize the result of that something — how are you going to say that something? — and use your practiced skills to turn your idea into a photograph which can be shared with others.