The official monetary unit in the Dominican Republic is the peso (signed as RD$ or DOP), which is made up of 100 centavos. The coins are in value of 1, 5, 10 and 25 pesos and the bills are 20, 50, 100, 200, 500, 1,000 and 2,000.
Exchange your currency at the bank or an official exchange kiosk (Casa de Cambio). Don't forget to take your passport when changing at a bank. Banks are open during normal business hours, until about 4 pm. You may also be able to use USD or Euro, but be careful not to over-pay. If you change your money in the resort you can be sure you get a very bad deal. Google the exchange rate by entering "us$ to Dop" or "Eur to DOP" in the search box to check the exchange rate of the moment.
No business in the Dominican Republic will accept Travelers Cheques. You can only cash the cheques yourself at a local bank.
In Punta Cana it will cost a business about 16% in fees for a payment with credit card, so not that many businesses accept credit cards. In this country cash is still king.
In February 2014 the exchange rate was as follows:
The Dominican peso has been slowly declining over time; in last 10 years it hit the historic low of 16 RD$ per US dollar (14 RD$ for 1 Euro).