Tunisia's main airport is Tunis-Carthage (TUN) but international flights - including many European charters - also fly to Jerba (DJE), Monastir (MIR), Sfax (SFA) and - for the Sahara - Tozeur (TOE).
Airlines
There are no direct flights from the US to Tunisia so your best bet is to fly via Paris' Charles de Gaulle Airport and connect on either Air France or Tunisair, which both offer frequent flights to the country.
Flight Times
Flying from New York to Paris takes about 7 hours; flights from there to Tunis take 2-1/2 hours. From San Francisco add about 7 hours.