You will use a card called the "Key to the World Card" (aka KTTW card). You have to link a cc to the KTTW card in order for that KTTW to be able to be used for essentially unlimited charging purposes. However, you can also say that you will be responsible for a person's KTTW card (e.g., for the whole family, for the spouse, etc.). However, each person can have their own cc set up if they want. If you are a parent, I think you can also deny charging privileges for children. If you don't have a cc linked to it, I think you will be considered "cash" only in which case you will have charging privileges up to a certain limit. I think it's around $500. If you have a cc linked to the KTTW card, they will bill your cc every $500 during the trip. If you have a cc set up, you won't need to visit guest services to "settle" your final bill. However, if you don't have a cc set up and there's an outstanding balance, you'll have to settle it before you can get off the ship.
Note that unlike Walt Disney World, you can bring Disney Gift Cards and preload them to your account (instead of accruing a balance first and pay it off), or call ahead of time and have it loaded onto your account. I only mention this because you can buy discounted gift cards (see the Budget Board) pretty easily for at least 4% to 5% off, with sometimes 10% off. Of course the risk is that you may be stuck holding on to the GC if you don't go on the cruise. However, you can use it for WDW.
For your folio, you can now view all of the charges on the phone app. However, you can go to guest services to request a paper copy. I strongly suggest you check the folio and look at it closely as there have been glitches in the system (phantom charges) with the move to the app system for folios. If you don't check,
DCL isn't going to check for you. In the last trip we found a $100 error.
One last thing, for drinks that you order, there's an automatic 18% gratuity already added in there. You may be asked again for "additional gratuity". However, note that would be on TOP of the 18%.
Ok, one more thing. Don't forget to book an On-Board Placeholder for a future cruise for $250. You can only do it onboard and you get a 10% discount on a future cruise. You will just have to use the placeholder after you leave the ship to select the sailing that you want. It's good for 24 months from when you book, but is completely refundable if you don't use it.