Tours are prepaid so you'll only need money for drinks, laundry, souvenirs and tips; for this, bring cash. There are ATMs in most main towns, but it would be wise not to rely entirely on being able to use plastic. Credit cards are accepted in some hotels and souvenir shops, but only in major cities or well-touristed areas.
The unit of currency is the ngultrum (Nu), which is pegged to the Indian rupee. The ngultrum is further divided into 100 chetrum. There are coins to the value of 25 and 50 chetrum and Nu 1, and notes of Nu 1, 5, 10, 20, 50, 100, 500 and 1000. The Nu 1 coin depicts the eight auspicious symbols called Tashi Tagye, while each note depicts a different dzong.
Indian rupees may be used freely anywhere in Bhutan (don't be surprised if you get change in rupees). Officially 500 and 1000 Indian rupee notes are not accepted due to large amounts of counterfeit notes; however, in practice 500s are usually accepted. Ngultrums cannot be used in India.
It is OK with the Bhutanese if you bring a reasonable amount of Indian currency into Bhutan, though Indian regulations prohibit currency export.