Tips to applying eyeshadow:
First things first. Choosing the right color. You will want to choose a color that is compatible with your eye tone. The best colors for blue eyes would be rich browns, soft peaches, and golds. The best for green or hazel eyes is warm browns, deep purples, and even emerald green to play up the eyes. Brown eyes can be played up with most any color. It is nearly impossible to go wrong.
The simplest tip to apply eyeshadow is to choose a neutral tone, and apply over the entire lid, crease, and just slightly above.
To polish up that look a bit, put a neutral tone on the lid, and apply a bolder tone (in the same color scheme, or that is complementary to the neutral tone) to the crease and slightly above.
There are several good tips for applying eyeshadow.
One would be the technique of the "smokey" eye. Start of with a neutral gray. Apply lightly over the lid. Then select a bolder, darker tone of gray, and apply to the crease. Apply a lighter, silver tone to the brow bone, and a dark charcoal tone to the outer corner of the eye. (it is highly recommended buying the four gray tones in a package, or asking for assistance when purchasing the eye shadow. Throwing together any random gray tones that happen to meet the specifications would come off with an unattractive look.)
Some other tips to keep in mind would be if you are planning to wear a bold lipstick, keep the eyeshadow to a light neutral color.
Making eyes pop is fairly easy. Either apply a shade that is similar to your eye tone, or use a complete contrasting color. (blue on blue. Or jeweled blue on a deep brown.)
Never put a dark shade on the brow bone, unless you are making a fashion statement.
One last thing. Blending is key. Blending colors gives the eye a smooth look. Without blending, the eye shadow looks choppy and comes off unattractive.