To gain entry into Tanzania, US citizens and most other nationalities will need a passport and visa. The passport must be valid for 6 months after the intended length of stay.
Visas can be obtained prior to departure from the USA (recommended due to long wait times at JRO) or at your point of entry into Tanzania. The visa cost for US citizens is $100. More information can be found here: http://tanzaniaembassy-us.org/?page_id=76#visaForms
To obtain the visa upon arrival at the airport, you will need your passport, the flight card (given to you on the plane), and US dollars. The visa cost for US citizens is $100 and $50 for most other nationalities.