As long as your organization has Gift Cards enabled, you should see Gift Card as a payment method listed when trying to apply a payment to a balance.
From the Unpaid tab of a Unit, select the items that you need to apply payment toward. Next, select the Pay/Schedule button.
After selecting 'Gift Card' as the payment option, input the gift card number.
Note: Gift cards cannot be used to make partial payments. For both staff and members/participants, the gift card must cover the whole amount OR the amount must be split so that two separate transactions can cover the due.