Virtually all ships are a cashless society . When embarking the ship you are given a card that accomplishes three things. 1) it is the key to your room 2) it is your "ID" for getting on and off the ship and 3) it is your on board charge card. As you board you will be asked to give a cash deposit or major credit card to establish your on board account.
The card is then used to charge your drinks, shop purchases , spa treatments
and anything else you "pay for" on the ship. That same account will have any shore excursions you purchase through the ship on it. If you pay by credit card, they simply charge the card at the end of the trip (all ships have various methods of reviewing your bill prior to final settlement). If you pay by cash, you settle your bill on the last night.
Can you pay every day? I don't know why you would, but I presume the pursers desk would take a payment against your account.
Does this answer your question? If not, please feel free to ask more.
Have a happy cruise, relax, you may be new, but the staff on the ship is not and they are there to make you happy in every regard.
I can answer specifiacally on the Legend since I just got off her on May 29.
They were announcing that if you had a balance on your account and had paid by cash
you would get a check in the mail within a couple of days. The reason they do not
refund your cash is that from that point on your account would be closed and you would not be able to drink etc. on the last night out.
What ship will you be on. Royal Caribbean has a feature when using the cabin TV, you can access your account and actually get up to the minute balances of all your charges, great way to keep track of what you are spending.