The only place to directly use gift cards is in the shops (and I'm not sure it's possible even there). The easiest way to use gift cards is to bring them to Guest Services to be applied to your account as soon as you have an amount equal to the gift card value on your account.
Charges to your onboard account include excursions booked through Disney, which will be on your account when you board; gratuities, which will be on your account a few days before debarkation; and onboard activities (nursery, spa, adult dining, beverage tastings, BBB, extra-cost beverages, shops, and so on), which will be on your account when they occur/are purchased.