Tilt your chin down to get a better look at any dark circles rimming your peepers. Then, mix a droplet of makeup primer with your concealer in the palm of your hand. This combo works great to moisturize the eye area and helps create full coverage that's still lightweight.
Dip a concealer brush into the concealer-primer mixture, and apply some to under-eye circles, starting at the innermost corner under your tear duct. Gently blend the concealer outward toward the cheekbone. Do the same to your eyelids, blending concealer outward with the brush. Cover the skin from the lashlines up into your brow bone, since lids tend to get red or veiny when you're stressed or sleep-deprived. If needed, use your finger to gently pat the concealer into skin until it's fully blended in.
Dab concealer onto any reddish or discolored parts of your face -- usually the areas around the nose and mouth. Use the brush to blend the concealer into skin, or gently pat into skin with a makeup sponge or your finger.
Dust some translucent powder over the spots you've just concealed around the eyes, nose and mouth. Make sure not to drag the brush over your face, since it will sweep the concealer off the spots you want to cover up.
Apply another thin layer of concealer with your brush or finger if you still notice dark circles or discolored spots. Set the concealer again with a light dusting of powder. Whatever you do, use a light hand with this second layer to avoid cakey makeup.