Using a gift card to capture a payment is very similar to capturing a payment for any other payment method. The only difference, is that you will be required to input the gift card code that is being used at the time of payment.
From the account screen (where payments are captured), click on 'Add Payment':
Once you have confirmed the amount and any tip, change the payment method to 'Gift Card'. When you do this, a field will appear asking you for the gift card code:
As you type in either the client name, or the gift card code, you will see the available gift cards appear, with their remaining balance. Click on the gift card you want to use, and click on 'Add Payment':