To get rid of dark circles under your eyes take a few ice cubes and wrap the ice cubes in a clean washcloth and apply the washcloth to your eyes until the ice melts.
The ice will help get rid of the dark circles under your eyes but may take a few tries to get them to go away.
You can also place cold cucumber slices over your eyes to remove the dark circles or apply a cool washcloth.
If you want to use an over the counter cream to remove the dark circles then the best cream I find that works for me is L'Oreal Paris White Perfect Magic White Double Whitening Eye Cream.
Apply the cream daily or nightly until the dark circles go away.
For me it took a 4 days to start really seeing results and within a week the dark circles were no longer under my eyes.