From Madrid to Segovia:
There are many trains and buses. Choose the most convenient for you. Form the airport, it is easier to go to the train station, but the train trip to Segovia takes longer:
Train:
train departures every 2 hours from different stations in Madrid. The trip takes 2 hours and the price is 5.65 €. See the timetable here. If you come from the airport, take the metro at the airport (Line 8) and go to Nuevos Ministerios (no transfers, 15-20 minutes). There take the train to Segovia.
Bus:
buses are more frequent. The trips takes 1 hour and 15 minutes and the price is 5.85 € See the time table here. Remind that may 2nd is the regional holiday in Madrid, so you have to look for the buses with an F (Festivo) in the column Periodo de Circulación. Buses depart from Paseo de la Florida 11 (close to a hotel named Florida). Metro Principe Pío (lines 6, 10 and R). To go from the airport to this bus station, take the metro at the airport (Linea 8) and transfer en Nuevos Ministerios to Line 6. Then go to Principe Pío (around 25 minutes).
Here you have a map of Madrid metro.
In Segovia, either from the train or the bus station, take a taxi to the Parador.
You can see in this google map, the location of the train station, bus station, Parador, and other interesting places in Segovia.
