To conceal the darkness under my eyes I use Benefit's Erase paste, applied with a small brush.  Then I pat it on my undereyes and extend it to my upper lids as a primer for eyeshadow.  The key is patting it on rather than smearing it.

I think it's very helpful to catch up on sleep, that'd not only make you look more alert but also feel more alert. But if you must resort to makeup, look around the reviews for good under eye concealers. Those can help mask it and give your eyes a youthful glow. 

I have dark circles as well.  Benefit's Boi-ing works for me, the erase paste didn't conceal well enough.  Good luck!

Lancome has a really great liquid concealer that comes in a little tube. It gives great coverage without being too heavy. Plus the colour matches my skin colour perfectly so it looks great every time!