When you check in at the port you must assign a credit card to your shipboard account. Everything on board that is purchased by you and your family is put on your shipboard account using your Key To The World Card which is also your room key.
At the end of the cruise you have the option of leaving everything on your credit card or paying it off in cash, travellers checks, Disney Dollars. You will get a print out of all your charges on the last day, but you can also get a print out at any time by going to guest service desk and asking.
MJ