If your mint came in a plastic clamshell container, just pop that right in the refrigerator. Your mint should last over a week stored this way. Alternatively, store your mint refrigerated in another type of sealed container.
Or, like many other herbs and veggies that come on a stem, cut the bottom of the mint stems on a diagonal. Place in a tall jar with about an inch of water in the bottom, cover the jar loosely with plastic, and place in the refrigerator. Change the water every few days.