If a customer pays for membership (e.g. 5 classes) and cancels a class before the cancellation cutoff time (an option you can control in Settings>>Registrations), then the customer will be credited back one of their classes.
If the customer paid for that individual class via a drop-in (non-member price), and they cancel, they will receive the payment back via the same method they made the initial payment with.
If in either case, the cancellation is after the cutoff time, no refund of the membership credit or the payment will be made. The customer will appear on a late cancellation list on the class attendance report.
To see this, head to Customers>>Report>>Customer attendances. Once here change status to 'Late Cancellations'. Once done click 'Go' to show results):
You also still have an option to forgive the late cancellation and manually make the refund.
To do this, go to Customers>Customer List. Once here you can select the relevant customer's name, which will take you to their profile page. Select payments and scroll down the page to payment history, and refund the relevant payment.