I thought I'd see a big blue button to push, but I found just a little sentence with the amount due and a link under my resort name on the first day of My Plans.
If you want to pay with gift cards than you should call Disney to make a payment ahead of arrival, otherwise, they will charge the balance due to the credit card on file, usually before you arrive at the resort. If you call to make a payment then there is an automated payment option which will take your gift card payment without having to wait for a live person. If you don't pay the balance due before arrival and your credit card is charged then you will still be able to have the charges reversed when you arrive at the resort. But that is more annoying and time consuming than just calling Disney to make the payment ahead of time.