In my opinion changeable or stormy weather gives some of the best chances of a good photo and the warm low light of dawn and dusk the best time of day. In fact photographer Freeman Patterson says that "edges" often give the best photographs, whether of the land, the weather or the day. All seasons can give good opportunities but high summer is the least promising. For trees and leaves the fresh greens of spring before the leaves darken and the spectacular colours of autumn are often best. Mountain environments often look better once the bracken has changed to red and grass to yellow. Clarity will be best after rain or when airflows bring cold dry unpolluted air. The light is everything !

Wide angle lens
Wide angle allows two things, a wide view to include a strong foreground and deep depth of field to enable foreground and background to be in focus. To obtain maximum depth of field use the smallest aperture possible. (By setting the infinity marking on the focus ring to the depth of field marker for the aperture being used, the maximum depth of field that includes infinity will be obtained, the hyperfocal point). 

Telephoto or "long" lens
In landscape the function of a long lens is not only to bring things closer but rather to eliminate depth and compress distant objects into a closer relationship with foreground objects. Taken to extremes this can result in an almost abstract image .Its shallow depth of field can be used to isolate one object in a complex picture.

People
Inclusion of figures in a landscape is a personal thing, I rarely include them but they can be used as a focal point or to emphasis the scale of a landscape and a sense of isolation or to encourage an emotional response in the viewer.

Repetitions and patterns
It is worth looking for repetitions that can be emphasised in an image, often with a telephoto lens.

Leading into the picture
It can be helpful if a path or ridge can be found to lead the eye into the centre of the picture.

Sky and horizon -rule of thirds
The classic position for the horizon is probably a third way down the picture. I would urge you to abandon this approach and include sky based upon its interest. Plain blue (or even worse) grey skies being excluded.
 However the rule of thirds has its place in positioning objects within the frame, although always be ready to abandon it.
 
 
 

A philosophy
The camera must become an extension of your body, with its controls manipulated instinctively and intuitively. Your consciousness becomes its consciousness. The art lies in communicating  your soul though the fall of light in a suspended instant of time, look for those moments at the edges, of day and night, land and sea, forest and plain, city and country, life and death. Look for the deep song of the visual world. For the duende. Search also in the details, in the detritus of a tideline, in the crystal of a snowflake and in the emptiness where less is more and perfection is obtained when nothing else can be removed. 
And remember the lens cap! 
 

Cameras & equipment
Camera features are not very important. Any 35mm or better format that allows manual control of exposure and focus is suitable. For mountain photography light weight, ruggedness and minimum reliance on battery power are further considerations.
A built in or independent light meter is essential and a tripod is useful, especially when taking long exposures to emphasise movement.  ( again)
Unlike camera features lens quality is of course important : I carry 17mm, 24-50mm zoom and a 70-200mm zoom. Polorising filters and lens hoods. I used to use 50 ASA Fujichrome film and scan my slides with a Nikon Coolscan V. I now use a 10 megapixel digital.
My digital lens setup is 12-24, 24-70, 70-300 (plus 170-500 if wildlife potential) to get about the same effects from a partial frame body as the film camera. (The 12-24 cannot accept a polariser). It is however much bulkier than the film setup, although part of that is not due to digital issues.

Dont forget Amazon UK when looking for photographic equpment (for SLR lenses, specify mount in search)

 

Sigma 12-24 wide angle (Nikon fit), an ideal zoom range for digital landscape 
 
 
 
 

Landscape photography books & photographic software