Applying eye shadow can be a little tricky. But it needn't be if you know the tricks involved.

Here's How:
Before you start, dust eye lid with a dampened brush and a little face powder. This will help to prevent your shadow from melting.
Choose three shades in the same color family - light, medium and a darker shade for contrast
Apply the lightest shade on the entire lid from brow to lash line.
The medium shade is going to bring out the color of your eyes. Apply from lash line to just above the crease.
The darkest color is going to be applied close to the lashes. Dampen the brush and then pick up a little color. Smudge it in around the lash base. If you have bags beneath your eyes, you might want to only line the top lashes.

Tips:
Use a touch of gold shadow on the brow bone to make your eyes look even brighter. You can use powder or one of those fat pencils. I have even used that liquid highlighter in a bottle and it gives good results too.
You might notice a tendency for your lids to appear somewhat crepey. This makes shadow application more difficult. To counteract this, stay away from bright colors. Subtley is what you are looking for at this point as softer colors are far more flattering and less aging.
Pearly shades are great for highlighting the brow bone and opening up the eye area.