You supply a credit card during online Check-In.
You can then stop by Guest Services and pay for outstanding charges during your cruise with gift cards
If you're buying multiple gift cards, it's easier for everyone involved if you use disneygiftcard.com to combine them into as few as possible. You can have up to $1000 per card.
I haven't waited long at Guest Services when I go during dinner/show time or shortly after reboarding on a port day. I typically wait until I'm sure I have or soon will charge an amount at least equal to the balance on my gift card and/or Disney Rewards card, then bring the card(s) to Guest Services to have the value applied to my account. Even one time when my credit card had already been charged mid-cruise, the cast member was been able to reverse the charge and apply the gift card.
GET UP TO A $1000 SHIPBOARD CREDIT AND AN EXCLUSIVE GIFT!
If you make your Disney Cruise Line reservation with Dreams Unlimited Travel you’ll receive these incredible shipboard credits to spend on your cruise!