Transport Madrid - Palencia

There are 3 ways of moving from Madrid Airport to Palencia:

+ By car:
Renting a car is quite cheap in Spain, specially if you are 2 or more people travelling together. You can rent a car in the airport through the main agencies (Avis, Hertz, Europcar, Alamo, etc. http://www.aena-aeropuertos.es/csee/Satellite/Aeropuerto-Madrid-Barajas/en/Page/1049727006477//Rent-a-car-desks.html), but also with other low cost companies like Firefly (https://global.fireflycarrental.com/) or Goldcar (http://www.goldcar.es/) (Always be carefull with these low cost companies, they are difficult to contact sometimes and it is important to check their Term and Conditions)
Also, there are several general pages for car rentals wich will offer quite good prices (lastminute.com, skyscanner.com, esycar.com, holidayautos.com, etc .)

I will post later how to get to Palencia by road.

+By bus:
There is a line from the Terminal 4 of the airport directly to Palencia twice a day (If you reach Terminal 1 or 2, there is a bus moving from those to T4 and back). Duration is around 4 hours and price around 35 euros. You can check it on www.alsa.es. It is a very good option if the timetable is close to your plane schedulle.
Also, you can take the underground (Metro) to the main bus station of Madrid and check the buses from the same web page, but it's alittle bit more complicated.

+ By train:
 May be is the best solution if you are travelling alone. The best option is to take an Alvia train from the Chamartin Train Station (also called North Station), you should get there by metro too. For trains in Spain www.renfe.com. Duration is around 1.5 hours and prices start from 16 euros.

I will post also about Madrid underground later.