Magento supports 2 types of refunds: Online and Offline. Online refunds will also refund the amount at the payment gateway. Offline refunds will only refund the amount on Magento.

An Offline refund is created when you click the Credit Memo button of the order from the Magento admin area. To perform an Online refund, you need to first find and click on an Invoice and then click the Credit Memo button of the invoice.

We include more details on how this can be done in our Magento documentation.