I think a big mistake women make when applying eyeshadow is not blending. My favorite way to make sure it's well-blended is to start with the lightest color and go to the darkest. Get the placement of the colors where you want them (typically, darker in the crease, but I'll talk about this later). Then, go back over your darker shadow with your ligher ones. So, light to dark and then back up to light, covering your whole lid with the lightest shadow. This will get rid of any harsh lines and also make sure your shadow isn't too dark. It's a great intensity controller.
As far as placement of shadows, you want to look at your eye shape. The ideal shape (or so they say) is almond. If you have that, you can do quite a few options - darker in the crease, darker on the outer corners, a light wash all over - almost anything goes for that eye shape. For other eye shapes, you're trying to manipulate the shadow to make your eyes more almond-shaped. Here are some examples (though by no means an exaustive list):
Deep-set: don't use a dark crease color - this emphasizes your deep-set eyes. Instead try a medium tone on your lid
Close-set: try putting high-lighter under your brow and in the inner corners of your eyes. Instead of a dark crease color, try using your dark color on the outer corners of your eyes.
Wide-set: this is one of the only eye-shapes where you want to use a darker color on the inside corners to draw your eyes together
Round: try using a darker color on your outer corners to elongate the eye. Don't line the bottom lid - this emphasizes the roundness
Small: don't use too much dark shadow as this closes in the eye. Try a medium shade on the outer corners.
Asian: don't try to make a crease with shadow, it's usually unnatural-looking. Instead, play up your beautiful eye shape by focusing on your lash line and mascara.
Again, this doesn't cover everybody and these are pretty much basics - there are NEVER rules in make-up, just starting points. If you're completely lost, this might help you out.
As far as eyeshadow colors go, a good place to start is to complement your eye color. Blue and green eyes look great with warm brown shadow, brown eyes look gorgeous with purples or blues. Play around with color and see how it affects your eye color. (For example, I have blue-green eyes. When I wear brown shadow, they look more blue and when I wear purple, they look more green.) For everyday, you want something that makes people say, "Wow, look at her eyes!" not, "Wow, look at her eyeshadow."