Concealer is a base foundation that can offset the color of a dark circle under your eye. Choose a color of concealer that has opposite tones of color from the tones that are in your dark circles. Use a color wheel to determine what colors are the opposite of the ones you want to conceal.
Using a dark eyeliner, draw a line about halfway or two-thirds across both the bottom and top of the eye, right along the lash line. Drawing all the way across your eye to the inner corner will make your eye look smaller, and possible closer together.
Use a a thick mascara that coats your lashes thoroughly. There are many different kinds of mascara, from thickening to lengthening to waterproof. Try out a few different kinds to see how they look with your eyes. Get close to the roots of your lashes, applying mascara at the lash line.