How to optimize sharpness in landscape photos
General Principles
Any lens has an optimum aperture at which it will be at its sharpest subject to design. On moderate quality lenses designed for 35mm film, that might be half-way through its range, say about f/11. On lenses designed for digital, it may be one or two stops wider, say f/8 or so. On expensive lenses designed for photo-journalists, it might be deliberately shifted towards the wide end (because they're forever shooting comparatively dark indoor press conferences).
If you stop-down too far, you'll start getting diffraction detracting from the sharpness.
First thing is to establish that optimum aperture. Chances are if you're working towards the end of a reasonably sunny afternoon, you'll be using something like (iso100, f/8, 1/250th) as an exposure - the equivalent of f/11 in Sunny-16 metering, say. That's playing into your hands already - it's going to be closer to the optimum aperture and it's faster than it would've been by a stop or two, too.
Next, calculate or estimate the depth of field. This is defined as the distances before and after the focal plane within which the image is "acceptably sharp", that being the circles of confusion cast by the lens are smaller than a criterion based on the intended viewing distance.
In practice, it suffices to know that at wider focal-lengths, you have huge depth of field, dropping off a lot as you zoom more. Ie, if you're shooting a wide-angle 24mm vista, you have depth of field from a very few feet out to infinity by f/5.6. If your lens has DoF scales, use them.
Finally, weigh-up the distances in your scene. Only if you have a boring shot with everything at infinity should you focus at infinity. Otherwise, you want to focus at a point slightly beyond the nearest object you want to be in focus - because the aperture will give you depth of field a little in front and a lot beyond the focal distance.
A distance at which everything from half that distance out to infinity is acceptably sharp is known as the hyperfocal distance. By focussing at this, you are not "wasting" any of the depth of field by letting it extend "beyond" infinity.
Tripods, etc
As a rule of thumb, most people can hand-hold a dSLR or 35mm camera at 1/focallength (35mm equiv) without introducing motion-blur through camera-shake.
For example, 1/125th will keep you steady up to 70mm zoom on a dSLR.
You do not need a tripod unless you go slower than this.
Some SLRs have "mirror lock-up", in which the mirror flips-up and stays put so that only the shutter needs to move to take the shot. This is useful, but also only if the exposure duration is of the order 1/15th to about 4 seconds; beyond that, either the shot is fast enough or slow enough that the vibration from the mirror-slap will not adversely affect the photo.
Digital Cameras
If you've been reading through this with a view to using a dSLR or compact camera, there are a handful of more specific considerations.
First, the chances are that the optimum aperture will already be fairly wide. That's OK, since the smaller sensor gives you more depth of field for a given aperture and focal distance than larger formats.
It would be ill-advised to stop-down to f/16 or f/22 on most lenses used with a dSLR, as diffraction will set in, worsening the image more.
Shoot RAW. Don't rely on the machine applying its own sharpening and storing as JPEG, which loses resolution, accuracy and colour-depth; by shooting RAW you're retaining as much image data as possible for later.
Large-format
Associated more with large-format cameras, but also present in some special (expensive) smaller lenses, are movements. Tilt movements can radically adjust how you focus and expose a photo.
Ordinarily, for most lenses unless specially designed otherwise, the focal plane is just that - a plane parallel to the film or lens planes, at a given distance away, at which every point is sharp, and the depth of field either side of it determined by the aperture. However, when you tilt the front standard forwards, the plane becomes wedge-shaped and rotates away from the vertical, with the thin end towards your feet. Similarly if you rotate it backwards, the top end of the focal plane comes towards you instead.
normal
with front tilt forwards
There is a significant change in approach required: no longer do you think in terms of "focussing on" a particular object; rather the interesting factor is how the focal plane/wedge intersects with the scene, what objects in it will be acceptably sharp rather than one specific distance. Be careful: too often, the effect of front tilt is described as "increasing DoF". It does no such thing. You will not get the illusion of an increased depth of field unless this rotated plane fits the scene better, both in terms of the objects near and distant, and the lack of critical subject-matter perpendicular to the focal plane beyond the depth of field.
For the record, swing is just the same as tilt, but rotated about a vertical axis instead of a horizontal one.
With tilt or swing, a similar effect can be achieved by rotating the rear standard in the opposite direction; however this will additionally distort the image perspective.
Comparison
Digital cameras (at least the affordable ones) have a small sensor, giving you comparatively lots of depth of field for a given aperture. This makes it slightly harder to acheive differential focus, ie a narrow depth of field, but it does mean you don't have to stop-down so far to get reasonable landscapes, hand-holding in bright light. However, there are some scenes where you have to stop-down an awful lot, when you'll get diffraction working against you.
Larger-format cameras do not give so much DoF at the same aperture, but you can typically stop-down a lot further before diffraction sets in (eg f/32 to f/45), and you can tilt the focal plane so it intersects the scene in optimal, or creative, ways.
Digital Processing
Now you've done the best with the image out in the field, you can start considering unsharp-masking USM in PS. There are two distinct ways to use it: first with a high amount and narrow radius (eg 100, 1, 1) to give fine detail, and once the opposite, to improve local contrast (10, 40, 1). Adjust numbers according to image-size and taste.
Finally, an example: 
, Sunlit Evening, Perthshire.
According to the exif information, that was 1/125, f/5.6, iso 100, 24mm focal length. Hand-held, no tripod, focussed on one of the baby trees nearby along the left side, pine-needle-sharp all the way from nearest heather to infinity.