Wow - Landscape is such a huge and varied genre of photography... I teach landscape photography at Mohawk College and even after 30 hours, there is still so much more to discuss and try.
One of the difficulties students have is in visualizing then building landscape photographs. They see a great scene, raise the camera to their eye and shoot then wonder why it does't have the same impact. What they forget is that the photograph can only represent what they see; the photograph falls short of their memory of the scene because they haven't built into the photo all the other "cues and clues" as to what the day was like and what details they saw in the scene that weren't captured well.
I always advocate working towards creating strong 3-dimensionality. If you have a grand scene or vista before you, it needs to be set into the context of what's on the ground in front of you which will provide the necessary context for those viewing the photo. This is done by actively searching for then building into the composition a strong (detailed, textured, interesting) foreground element which is often called a "foreground anchor".
Your work continues as you work to "unite" the foreground and background by actively looking for and incorporating leading lines to guide the viewer through the scene from foreground to background: pathways, fence lines, trails, roads, river banks, etc. C-curves, S-curves and especially diagonals are the strongest shapes to work with.
As you do this, keep in mind your "rule" of thirds to help with the initial design and layout of the composition. If the sky is strong (great clouds or colour contrasts), then keep the horizon low in the composition, but still with leading lines and all. When the sky is weak (overcast or only a monotonous blue swath) then de-emphasize it by placing the horizon higher in the frame.
As far as lenses go, more often than not I start with the widest focal length (in my case 24mm). I leave the zoom at tis widest setting and work at creating my composition at this wide perspective because of the great 3-dimensionality created by wide angles. That's not to say landscape can't be made with telephotos - of course they can and very effectively - but telephotos tend compress distances, shortening mid-ground areas and eliminating foregrounds creating very different landscapes.
To maintain details from the foreground to the background, a small aperture is used (for APS and 4:3s sensors f/11 and less often f/16, but not smaller due to loss of sharpness from diffraction). With full frame and larger sensors, f/16, f/22, even f/32 are usable. But these small apertures combined with low or native ISO (typically 200) result in slower shutter speeds, so a tripod is essential along with mirror lock-up to prevent vibrations reducing image quality.
All of this means that you need to be observing far more than you are photographing. Being a visual art, you need to spend time building photographs in your mind before looking through a viewfinder. A viewing card (a black 4x5" card with a viewfinder cut out of it) helps with this process. Hold it close to your eye for wideangle and further for telephoto.
Something that too few people appreciate is the importance of the ambient conditions - time of day, time of year, weather conditions, etc. - for adding to the mood of the scene. You want to be aware and take advantage of these conditions as much as possible. That often means photographing when everyone else is sleeping, having breakfast or having dinner! And don't shy away from inclement weather - there are great opportunities when it's raining or foggy out. The American photographer Weegee once said "f/8 and be there". Nothing can be truer!
One of the best ways to learn how to make landscapes is by really examining and "deconstructing" landscapes made by other photographers. As you look at it, try to tease apart the technical details of focal length and aperture while looking for the visual design elements: leading lines, shapes and composition. Keeping asking: what makes this landscape work? How am I being drawn into the scene? What pathways am I following as I look at this photograph? What decisions has the photographer made to make this a compelling landscape?
Hope all this helps. Landscape photography is a wonderful way to spend a few hours (days, months, years...) in the great outdoors!