The currency is the Tanzanian Shilling. However, US dollars are widely accepted, as long as the print run is past 2007. Most places will generally give you change in USD if you pay in USD, and TZ Shilling if you pay in Shilling, even when shopping at those smaller shops and vendors.
All tourism services will accept USD, and the guides usually welcome tips in USD. If possible, travel with smaller notes. They also generally accept credit cards at most properties with telecommunications signal. However, it's usually better to use USD for tipping and purchases from markets, etc. Many vendors do not accept American Express, and it will be a good idea to travel with either Visa or MasterCard.