The credits are on your 'Key to the World card' which is your is also your room key, charge card (if you have charging privileges) and admission to the parks. When you settle your bill it states how many credits were used for that transaction and gives the remaining. Counter service on counter service receipts, table on table service receipt, and snack on snack receipts.
You only need one card to pay for everyone on the DDP in your party.
concierge desk can give you a print out of what you have used & where, as well as what credits you have remaining. there are occasional mistakes with credits, so you should keep track of your receipts & check them with each purchase