Discover makes it easy to cancel a credit card and close your account. All you need to do is call the helpline at 1-800-DISCOVER (1-800-347-2683). There are no fees for closing your account and you do not need to clear your account balance before you close your account. However, you will need to continue making payments on your balance until it is cleared.
Bear in mind that before you close your account, you will need to redeem your rewards. If you close your account before you redeem your rewards, Discover will credit you with your balance, but you will not get to decide the most preferable redemption method.