Go to
www.renfe.es and see the timetables (cercanias and regionales)), there are less trains in that type of days, but there are plenty of them. You can buy the tickets in the station counters or in the electronic machines (this sations are big, especially Villalba). It is not necesary buy the ticket to Segovia in the airport, (the seats are not reserved, you can seat where you like) the train is called regional but it is a normal Cercanias (short distance) train.