Everything is charged to your cabin account which you have to settle before leaving the ship either by credit card; travellers cheques or cash but if you opt for cash you usually have to put so much upfront at the check-in stage. Most cruise companies have the TV in your room set so you can see the how much you are due anytime. It is important to keep all the receipts you receive for drinks; wine gifts from the shops etc in case you have a query. If the TV facility is available then it is possible you can dispose of these receipts the following day once you have checked the entries on your account are OK. The advantage of paying by credit card is you don't have to go and join the queue to pay your account, but if asked let the card company do the currency exchange rather than the cruise company if payment is in dollars. If more than one person will have the right to charge out items you will need to arrange this, which could include your partner or children in some cirmcumstances.
You must make sure that you have a credit card with you, We were told by our tour rep that we would be able to use or Switch card but this declined on board as they only use Credit Cards, before you boad you will have your photo taken and it is at this point that you will register you credit card, each adult member will be issued with an on board credit card which you will have swipped each time you make a purchase regardless of wha you are buying, whether it is in the shops or the bars, the night before you arrive homm your bill will be waiting for you pinned o your door, this will allow you to check each purchaes, get ready for the shock, our most expensive purchases were the trips, next time we sail we will not purchase the trips on board but pick up a taxi at the docks as soon as we disembark. Enjoy your trip.