Image Sharpness - The Critical Factors

Sharpness is one of the hallmarks of photographic competence. You can argue, validly, that we get a bit too obsessed with sharpness since some of the iconic photographs of history aren't all that sharp. Composition and emotional content win over sharpness any day. But let's consider that a given. All other things being equal, I'd rather have a sharp image than a soft one. Here's a list of key things to manage in order to get sharp photos:

• Camera Technique. I have described before how to hold a camera in detail. You can learn how to do it in about 5 mintues and it will noticeably improve you shots.
• Shutter Speed. This is a biggie. If you're holding your camera correctly and still not getting sharp images, the next most-likely culprit is that your shutter speed is too slow. The rule of thumb is that your shutter speed should be no slower than the reciprocal of your focal length. In English, that means if the focal length of your lens is X, then your shutter speed needs to be 1/X or faster. And that's just to overcome camera shake. You'll need a faster (potentially much faster) speed if your subject is not stationary. Raise your ISO if necessary in order to get the shutter speed fast enough! ISO noise can be improved in post; bluriness can't.
• Aperture. Lenses typically are a little soft when wide open. Also, the narrower the depth of field, the more critical it is to nail the focus point since more of the picture is going to be outside the focus area. If possible, stop down the lense so that you're shooting in lens' "sweet spot" of sharpness and you're working with adequate depth of field. The challenge is that smaller apertures can run counter to using an appropriate shutter speed. It's a trade-off, but if you're prioritizing sharpness, most of the time you're better off compromising on the aperture in order to get a fast shutter speed.
• Subject. When you're learning to shoot, it's common to take subject-less pictures just for the practice. That's cool. But the problems with that are 1) the camera focuses on whatever happens to be under the focus point, and 2), a viewer of your photo is going to have no idea what should be in focus and will therefore expect everything to be in focus (anything less and it looks like the photographer screwed up). So I recommend always having a definitive subject in photos that aren't practice. Even in a landscape, I like to place an object (a rock, a tree, etc.) at the hyperfocal distance to make my subject and focus on it.  The hyperfocal distance is the closest distance at which your lens (for a given aperture) can be focused while keeping objects at infinity acceptably sharp. For landscapes, I'm often using my Tokina 12-24mm lens zoomed wide to 12mm and set to f/11.  At that aperture and focal length, I've memorized the fact that the hyperfocal distance is just over 2 feet, so I compose my shot so that there is an object about 2-3 feet away that I can focus on. For a landscape, this foreground object has the added benefit of imparting a great sense of depth to the photo. 
• Focus Point. For people or animal pictures, focus on the eyes. If you nail that, the shot will work even if everything else is out of focus. For other objects, put some thought into what part of the subject needs to be in focus. This is especially critical when you're working with a narrow depth of field due to a small aperture, a close distance to the subject, or a long focal length.
• Light. This is another biggie. Low light causes all kinds of focus challenges: slow shutter speeds, ISO noise, lack of specular highlighting, as well as poor auto-focus reliability and accuracy. Not only that, but low light is often ugly light. Not always, but often. People shoot in low light and their images are soft, flat, noisy, and lack color. Then they think there's a problem with their camera. It's not the camera; it's unrealistic expectations! All of the problems can be overcome by adding more light - by turning on some lights, opening curtains, or waiting for a different time of day. If none of that is possible, break out the flash. It was a watershed moment when I realized how off-camera flash enabled me to create beautiful light, instead of lucking into it.
• Manual Focus. Of course there are situations that have to be low-light (night-time shots, for instance). In these situations, auto-focus may just not work. Put the camera in live view mode, zoom in on the focus area, and then manually set your focus. Done. If your camera has focus-peaking, you may even prefer using manual focus over auto-focus because it removes any ambiguity about what your camera is focusing on.
• Tripod. If all else fails, break out the legs! The thing I like about tripods is that I can set my camera to optimize image quality (base ISO, aperture stopped down) and no matter what the resulting shutter speed, I'll get a sharp shot. Assuming the subject matter is stationary. If you're shooting landscapes, it's a must-have in my opinion.