You can pay by card in many places: big shops/supermarkets, but there are still many places which accept only cash: e.g. taxi (except for Uber in Bucharest), local shops, to buy bus or metro tickets. In rural part of Romania it is very likely that you will have to pay with cash. A recent development in Bucharest is that you can pay by card for a bus and metro fare.
Start by exchanging a small amount, the equivalent of 100-200€/$ at the airport or at the nearest Romanian entry point. As expected the exchange rate you will get in the airport is not that favourable. You can exchange bigger amounts once you get to a bank/exchange counter in a Romanian city.
Before leaving for Romania please do not forget to inform your bank to that you are planning to use your card during the trip in Romania especially if your bank card was issued by a non-EU(European Union) bank. This is valid for both your debit and credit cards. Otherwise you can have the unpleasant surprise of having the money on the card but not being able to pay. You could also check the fees attached to transactions in Romania charged by your home bank.
Make sure you have the phone number of your bank in your phone contacts so that you can get in touch with them from Romania in case of problems with your bank card. Visa and Mastercard debit cards (including Maestro) are widely accepted in Romania.