For paid orders, there is an easy one-click way to issue a full refund, and do subsequent cleanup like deleting the tickets, and re-adding those tickets back into the pool of available tickets to be purchased.
Locate the order to refund
Follow the tutorial here to lookup an order.
View the order, and click Refund
Original Payment: Refunds the money back to the payment method used, i.e. a credit card refund
Store Credit: Does not issue a refund, but rather adds a credit to the customers account, that can be later used in a different order.