Hi, how do I refund a customer who paid by credit card?

If they paid through QuickBooks Merchant, three options :

Go into the payment - select under Payment method "Transaction Processed", it will open a separate dialog box with "transaction receipt", refund option available at the bottom. 

Go into the payment - Bottom bar has a "more" option > Refund

Go to the + New > Refund Receipt - Make sure check box is checked to process refund.