By train, Salamanca is well connected to Portugal, Madrid and Barcelona. Check the website of RENFE
From the airport, catch the «Cercanías» (light rail) or Metro to «Chamartín» train station.
From Chamartín train station to Salamanca the fast trains (called ALVIA) take 1 hour 30 minutes and run 4 times a day.
By bus, you can book directly from the airport terminal through the web of AVANZABUS.
The bus takes about 2 hours 40 minutes from the airport.