The artistic aspect, including an interesting subject, attractive perspective/framing, lighting conditions, is obvious (but not always controllable by the photographer, e.g. at many sport events). So I’ll concentrate on the more technical aspects.
My “secrets” are (in order of priority):
1) Nail the focus on the main subject
2) Avoid camera shake
3) Avoid unintended motion blur
4) Get the correct exposure
5) JPEG only: Select the correct white balance
6) JPEG only: Select the correct contrast setting
ad 1) Many pictures live from their illusion of depth. This is not only achieved by choosing the appropriate perspective, but also the gradient of sharpness, which includes the choice of appropriate DOF (depth of field).
Obviously, for all this the main subject must be focussed properly to begin with. Casual focussing, such as let the camera choose the AF-point, misplacing the AF-point, trying to shoot (even only slightly) moving subjects with One Shot AF and the like, will often lead to mediocre results.
The same goes for shooting in P-mode (program automatic) instead of Tv, Av or M, because only the latter will allow you to control DOF and motion blur.
ad 2) If you stick with traditional wisdom, which states that your shutter speed should be the reciprocal of the focal length, you will rarely get a really crisp picture, even if you calculate in the crop factor correctly. These old rule of thumb was valid for viewing a picture at “normal viewing distance” and not as a 100% pixel representation on the screen, which is equivalent to inspecting a poster-sized picture closely. There is a reason, why valid resolution tests can only be made from a tripod, with remote shutter release and sometimes even mirror lockup. For practical use, you’ll have to factor in the closer viewing distance equivalent to viewing the 100% representation on the screen (and the actual steadiness of your hand).
ad 3) Whenever you have to deal with moving subjects, you would rather want the subject sharp and the proximity blurred and not the other way round. So track the target, thus reducing the relative speed of the subject and choose a short enough shutter speed to freeze the motion on the parts of the subject that should appear sharp. Once again, every estimation on the shutter speed required, will have to deal with the modern habbits of 100% pixel peeping instead of older experiences from the film days, where normal sized prints were viewed from normal viewing distance (e.g. closest viewing distance equals the diagonal dimension of the print). To stop action on fast and/or erratically moving subjects, such as dogs, children, football players and the like, you will rarely get away with shutter speeds slower than 1/1000s – provided you fill the frame with the action. A boring WA shot of the action, showing “everything and nothing” will need much less shutter speed, but will also rarely be judged as to be breathtaking.
ad 4) Crisp and sharp looking pictures should neither exhibit blown-out highlights, nor excessive noise. So it is essential to double check your exposure to fill the top region of the histogram without blowing any important highlights, such as white fur of a pet or light reflections on the cheek, nose or skinhead of a human.
Following the priority of my list, select ISO sensitivity high enough to get appropriate fast shutter speeds in order to avoid motion blur, but at the same time keep it as low as possible. Image quality is essentially the same from ISO 100 to 400, but above that, it starts to suffer slightly. In any case, it is far better to have an otherwise perfect shot with a little noise in it (that can be partially removed later in post processing) than a perfect clean and noise-free shot of a blurred subject.
ad 5) As we all know, light color controls the temper of a scene. For instance, a sunset captured with automatic white balance will look plain ugly. When shooting RAW, you will not have to deal with this, since you can choose the correct white balance later in the RAW processing without any adverse effects, but with a JPEG you will loose some precious color information if you have to alter the white balance in post processing.
If shooting JPEG, don’t stick to AWB since it is inaccurate in many situations. Make sure to dial in the appropriate preset and choose “Daylight” when in doubt – this way you wouldn’t be too far off in most situations (e.g. it would be the correct setting for the sunset picture).
ad 6) This also is only important if you’re not shooting RAW. For a punchy looking image, the correct contrast settings are important. These are also affected by the selected picture style. I would recommend to stick with “Faithful” with color saturation +1 for all shots. You will still have to adjust the contrast setting according to the scene, and this could be a little difficult, because the overall light situation does not always apply to a specific scene you want to capture. Generally, you should reduce the contrast setting if the scene shows high contrast and vice versa. But you’ll really have to check the specific scene you want to capture (best take a test shot and check the histogram), and not e.g. generally think “It is an overcast day, with soft light and low contrasts, so I can push the contrast setting all the way up for all my today’s shooting”…
You should understand by now, why so many people shoot RAW. It is hard enough to deal with all the other challenges, most of all being to capture the right moment, so they don’t want to bother with white balance and tone curves (which ultimately define the contrast too) and as an additional bonus they can deal with minor(or even major) exposure inaccuracies with the least possible degradation in image quality.
These are my “secrets”, and there may well be some more, but I believe these should be sufficient for the beginning, to get you the images you’re striving for 
