Get plenty of sleep nightly. Its not entirely clear why inadequate sleep results in dark circles under the eyes, but lack of sleep tends to cause the skin to become paler (thus increasing the appearance of darkness under the eyes), and reduces circulation. Its also believed that too little time lying down is a cause in itself. Before going to bed at night, remove all eye makeup. If you dont do so, when you get older, your eyes can look much more tired on a daily basis.
Determine how much sleep you need (its usually 79 hours per night, but varies for different people at different times throughout their lives). Try to get that amount regularly for a couple of weeks to see if that helps.