When you do online check-in, you can indicate which credit card will be used by which adult, and which adult will be responsible for purchases by any child (as well as whether the child is granted charging privileges at all -- if not, the only charges will be excursions and tips).
At any time after boarding, you can stop by Guest Services to apply gift cards, including Disney Gift Cards and Disney Visa Reward Cards, and cash to your account. Be aware that when your Key to the World card balance reaches a certain amount, it will be automatically charged to the credit card on file, so you should put forth other forms of payment as soon as you're sure you'll need them. It is possible to use a gift card for more than your current balance -- anything left over will be refunded to that form of payment (so don't discard a gift card until after you see the final balance at the end of the cruise).
