In the USA, cars are the most popular means of transport. Therefore, you will most probably drive the car of your host family. You need to clarify in advance issues of insurance and liability, which your au pair agency can also help you with.
As an au pair in the USA, one needs to have a driving licence. In this connection, au pairs should clarify whether or not Their driving licence is valid or if an international licence is required. The sponsor agency arranging the au pair stay can provide more information.
More on driving licence regulations in the USA is available on the website Transportation and Public Works.
Information about international driving licences can be found at automobile organisations or road traffic authorities in your home country.