This is a subject that is near & dear to me because I'm blessed with this problem to a certain extent. It needs to be addressed on two fronts.
1) Skin care. Moisturizing has been mentioned but I'm surprised there hasn't been a lot of talk about specific eye creams which are essential for the thin skin below the eye area rather than using a regular moisturizer there. I have tried many many many brands, mostly from department store counters because we all know the more you spend, the better the product will work, right???
Well this is true to a limited extent in that you get what you pay for but my expectations go higher the more I spend. The most effective I have found so far is this eye cream by Bobbi Brown...
http://www1.macys.com/shop/product/bobb ... slotId%3D2But the one that I'm currently using is this one by Shiseido...
http://www1.macys.com/shop/product/shis ... sn_resultsWhile neither has been magical, I have noticed improvement and shudder to think what my skin would look like at this point had I not adopted a daily skincare regimen in my late-30's (I'm 45 now, going on 29 if I had my way).
2) Concealer. A Bobbi Brown concealer was mentioned above but while I have not bought this one, I have had it used on me by their makeup professionals and the application seems a bit complicated. Again, I have tried a bunch of these products and my go-to is very simple. This Estee Lauder concealer...
http://www1.macys.com/shop/product/este ... slotId%3D2Paired with this Estee Lauder eye cream...
http://www1.macys.com/shop/product/este ... lotId%3D11The technique is to dab a bit of each on the back of your hand, mixing the two before application under your eyes. The eye cream helps to thin the consistency a bit which prevents caking and assists in a smooth application.
I learned of this by buying this little kit from Estee Lauder that had a foundation plus the concealer and a sample size of the eye cream...and a DVD which demonstrated this technique. It may seem pricey but you don't use a whole lot each time and as such, the eye cream lasts a long time.
Finally, one thing you could do to learn more is to get in the chair of a makeup professional and learn what they do. Good luck!!!