The best, quickest and most effective way would have to be a good concealer!! There are certain eye gels and eye contour creams (with light diffusing particles) which are supposed to diminish dark circles, but to find the best I would suggest asking in a large department store such as Boots, or try doing a search on Google for 'dark circles under eyes' you will find quite a few results.
get enough sleep! also drink lots of water as i think that it can be an indication of liver or kidney (can't remeber which) function... so it could be worse after a night on the tiles. touch eclat (radient touch) by ysl is good but a bit pricey at around 20 quid and eye masks can reduce puffyness.
I would definetly recommend YSL's Touche Eclat, its a liquid stick and its made for dark circle under the eyes. Make-up artists always recommend them and i think its a miricle worker. You will get it in any Boots stores for �21, good luck.
Dark rings under eyes can be an intollerance to a food or additive.
Chinese medicine says it shows a problem with the Kidneys.
First off drink lots of water, bottled not tap to keep flushing out those toxins. Don't go to a health shop fo allergy tests they re inaccurate at the best.
It takes a while for the darkness to go but I would suggest being referred to a nutritionalist.
They are also hereditary.