The process is the same for both a debit card and a credit card. The shop places a cancellation order with the card company, then the card company refunds the money into your bank account. At the earliest, a refund will take several days, but in some cases it can take one to two months. To have the refund process go smoothly, it is important to contact the store at which you made the purchase immediately. Confirm with the card company how long it will take for the refund to come through.