The Taiwanese currency is called the New Taiwan Dollar, while its currency code is TWD. Even though tourists can exchange money upon arrival at the three international airports in Taiwan, it is recommended that tourists exchange their money at one of the Taiwanese banks in a major city, because tourists may get better rates at the banks. The bigger hotels in the country also offer money-exchanging services. It is also to be noted that if you remain with any Taiwanese cash before leaving make sure to exchange it back to your currency because it isn't easy to exchange Taiwanese currency abroad.
Most of the places in Taiwan can accept credit cards, but small family-owned restaurants may only take cash. Though using credit cards may need for you to pay extra processing fees, which usually means that the shop you are buying your goods at aren't honest taxpayers. You just certainly avoid buying goods from such shops.
ATM's are very easy to find in Taiwan, they can be found at many 7/11 stores, banks offices in the streets which operate 24 hours a day and also department stores. Therefore it is very easy to withdraw cash in Taiwan, no matter where you might be. Also, most of the ATM's in Taiwan offer services in English, to make it easy for all tourists.