You can fly directly to Salamanca Airport. There are daily flights to Barcelona, Malaga and Palma de Mallorca (with Lagun Air and Air Nostrum). Another option is to fly to Valladolid Airport or Barajas International Airport in Madrid, the closest airports to Salamanca:
MADRID - SALAMANCA
Should you land in Madrid at Barajas airport, there is now a direct bus from Barajas Terminal T1 to Salamanca: see
Salamanca is 200 Km west of Madrid and there are regular bus and train services available.
VALLADOLID - SALAMANCA
Salamanca is 115 Km southeast of Valladolid and there is a bus service from the airport to the city centre. Regular bus and train services are available from Valladolid (city centre) to Salamanca.