To a new user asking about composition

There are no set rules for composition anymore, unless you make some assumptions. For instance Landscape is different in the Western and the Chinese tradition.
Therefore one can assume you will choose the first, and therefore you must know what Western painters did in the past.

But is your choice Landscape as a genre, or Portrait, or Still Life? Those are painterly genres, but Photography was not confined to that.

The Avant Garde in 1920-30 completely changed the painterly Rule of Thirds, which had been in charge before. It also started Street Shooting, where composition is rather in depth than on a flat    plane.
 According to D. Bate, American Street Shooting has evolved towards more Balance and Neutrality.

So this begs the question: are you opting for The New Objectivity of the American kind? It is only one option, but it is what most here assume, ignoring other choices, as we saw with Rodchenko. 

Photography, even of the amateur kind, is now globalised, and is branching in many new ways. Knowing about the past of Painting, and the reach of Photography, will open you many avenues of thought, and ways of shooting.

Composition is important but it shouldn't really limit your creativity, nor throw you towards the conventions of commercial genres, like Still Life for Advertising or Portrait for Marriage, the kind which go after money, and heavily use bokeh and Photoshop.

Instead please remember that the main gestalts, the psychological cores, were established at the Bauhaus, and that Andreas Feininger, (son of founder Lyonel Feininger)  used them to teach in his American books about Photography. They are the beginning of Modernity, so one might start from there.

Anyway shoot as much as you can, practice makes perfect.

As a postscript I found a picture of the celebrated Nature photographer Andreas Gurtsky, an example of the contradictions of even the simplest landscape:

Engadin, A. Gurtsky


Critic David Bate remarks that the composition is made in thirds, snow - mountain - sky, but then it is wrecked by the line of people in the foreground:
"It shows the awful consequence of mass tourism: humans as the blight on an other wise picturesque nature...the picture nevertheless depends on their opposing characteristics by combining them."

Has the objectivity of the Landscape being ruined by the subjectivity of the photographer, or is the environment showing us a different kind of objectivity that the photographer has chosen to report, with a social intent? 
Composition here signifies a lot, and the way you are willing to break it. Such a pure environment polluted by a colony of human ants!

Since Barthes wrote his essays on photography, no picture is innocent to me, it is always a sign of something else. 
For instance, the picture above for us signifies a negative, but are we sure it would do so to an Asian? From the beginning of Buddhist times mountains have been associated to public pilgrimages, like here:

So perhaps to an Asian eye the Engadin picture would automatically signify a positive. This is called a connotation, and is clearly culturally based. Globalisation has introduced another twist in the way we interpret the simplest images.

Additionally Westerners use perspective to convey distance, while Orientals use Atmospheric colour. The camera, which is a perspective device, therefore tends to impose the Western Order.
The Oriental tradition however is far from lost. You can see an example of composition by atmospheric haze in Chinese photogs. here and here. I find them among the most inspiring.

Aleksandr Rodchenko, the Revolutionary

“The modern city with its multi-storey buildings, plants, factories [...], all this [...] has changed the psychology of the traditional perception to a great extent. It seems as if only a camera is able to illustrate modern life.” (Alexander Rodchenko).

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We are all dwarfs on the shoulders of giants.

When Rodchenko began his career as a graphic artist under the Russian revolution he was already well known as a cubist painter, but his career skyrocketed with the use of the camera, one of the first Leicas, that he bought in Paris. Happy times when Leicas were still accessible to poor artists! The Leica could then be had for 133 roubles.

(Alexander_Rodchenko Wikipedia)

At a time when photographers were still stuck in the painterly debate between the Picturesque and the Sublime in the depiction of Nature, he famously declared that no picture should even be taken 'from the belly button level' and pointed his lens from plunging angles exclusively to cityscapes and the big demonstrations of the Revolution.

You might object to the ideology, and the rhetoric, but not to his impeccable visuals. It was the first time that proletarians got to see each other - bourgeois and the countryside having being the main subject of Victorianism - and so the tradition of social Reportage began with the march of Russian masses. 

Rodchenko graphical imagination was after the geometry of serial lines, in plunging perspectives, in stark black and whites,  in what came to be known as Constructivism: the city itself appeared as a giant factory. He was not far from F. Lang's 'Metropolis',  but in Germany  too a revolution had taken place, with the Spartacist days of Rosa Luxemburg.

In Russia Aleksandr gravitated in the highly progressive entourage of the poets Majakovsky, Osip and Lilya Brik - LEF, Left for Art,  their review was called - and it helped him keep the revolutionary momentum. He reduced his cubist paintings to monochromes, and then declared that painting was dead, in favor of the camera. There were rumors that Lilya offered her favors to Rodchenko while posing for advertising posters, but free love was usual then between comrades, so nothing shocking.

Rodchenko was a personal friend of Dziga Vertov, the outstanding film maker and inventor of Cinéma Vérité, photography never being far away of the documentary. How many talents fed each other in those early days of the Revolution!

Steel horses
steal the first cubes
jumping from the windows
of fleeting houses.
Swan-necked belfries
bend in electric-wire nooses!
The giraffe-hide sky unlooses
motley carrot-top bangs.
The son
of patternless fields
is dappled like trout.
Concealed by clocktower faces,
a magician
pulls
rails from the muzzle of a tram.

(From street to street - V.V. Majakovky)

A small Leica indeed allowed Rodcenko to record the city and its masses from a birds-eye POV which had never been attempted before.

Painting was to undergo a similar destiny in France and the US, but only 20 years later, with Informal Art and Klein's monochromes. So often revolutions speed up changes in art too.

 Rodchenko was also in touch  with Moholy-Nagy of the Bauhaus. Together they started  industrial art and design. Later however he was accused of having copied the Germans. Small minds!

I had a similar experience in the 1970s when I rediscovered Futurism. By using abstract décors like Balla had done, and by doing away with actors, we introduced installations and performance into theater. A Tabula Rasa took place in 1977-1979, with Teatro di Postavanguardia in Rome. A renaissance that was to last only a few years, before our funds were cut.

Rodchenko had showed that Landscape was just a bourgeois convention. We abolished the scene, and so the spectators became the actors. In Rodchenko pictures the actors were everyday people and thus he also launched Street Shooting, in a far more radical way of what had been  attempted  by Eugène Atget in his documentation of Paris.

Certainly the Leica, replacing the view camera, helped to catch the decisive instant, without the need for Atget's poses. The dynamic lines showed History in Action.

(Girl with a Leica)

Rodchenko also identified diagonal lines as the internal contradiction in respect to the square lines of the frame, thus a metaphor of movement. By destroying static lines he suggested the the breaking down of the image in lesser elements, doing away with the illusion that a picture is an innocent holistic reproduction of Nature. Realism, as an ideology, went out of the the window too. Bodies appeared  estranged from the conventions of the Portrait.

Rodcenko had a heavy price to pay for these innovations: during the purges he was put under trial and accused of 'Formalism': thus to have betrayed the Party and the masses.  It was a terrible accusation, therefore he was threatened to give up all his official jobs.

 So  after shooting for a while the Regime's celebrations he stopped, and began instead to work as a curator of other photographers, who celebrated the achievements of  Socialist Realism and the Five-years Plans of the Regime. 

The same Return to Order was taking place  with the celebratory 'Olympia' in Berlin under Hitler, and in the Fascist regimes, with their notion of a National art opposed to Degenerate Art, cultural hypocrisy being well spread on the surface of the planet.

BTW the plunging, slanted lines of Rodchenko have resurfaced, almost as a trademark, in the Freestyle type of shooting skateboarding in the Social Medias. It is even apparent  in the selfies of Smartphones, all gravity being lost in the Space Age.  

And yet even now  I still have to remind myself not to fall in the old convention, so strongly the tradition of a straight horizon  is entrenched in Landscape. Instead  one must use geometry to advantage, but not necessarily in a Naturalist way.

If you want to understand and learn to deconstruct the main genres of photography, beginning from Portrait and Landscape, those two genres laden with commonplaces, you'd do nothing better than read "Photography, the key concepts" by David Bate, of Westminster University.

To him Landscape is almost invariably an artificial construct built with an aim to order. No picture is an innocent search for beauty. He considers the 1930 as a key period, mentioning a parallel with the American f/64 group. here

On the other hand Old Europe, which is never really so old, did a beautiful Rodchenko retrospective in Summer 2013 in Vienna, at the Westlicht Gallery.

They had some of the best Rodchenko's quotes:

“Photography – the new, fast and real reflection of the world – should make it possible to map the world from all points of view [...]. In order to educate man to a new vision, everyday familiar objects must be shown to him with totally unexpected perspectives and in unexpected situations. New objects should be depicted from different sides in order to provide a complete impression of the object.”

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“We must revolutionize our optical perception. We must remove the veil from our eyes.”

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“Contradictions of perspective. Contrasts of light. Contrasts of form. Points of view impossible to achieve in drawing and painting. Foreshortenings with a strong distortion of the objects, with a crude handling of matter. Moments altogether new, never seen before… compositions whose boldness outstrips the imagination of painters… Then the creation of those instants which do not exist, contrived by means of photomontage. The negative transmits altogether new stimuli to the sentient mind and eye.”

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Alexander Rodchenko