You can take the Metro (Underground) at the airport terminal to reach the railway station Chamartin. The price is Euro 1.10. You have to take the train to "Nuevos Ministerios", line 8. Once there, you have to change to line 10 to reach "Chamartin", where you will have to take the long distance trains to Albacete.
You can also take the bus number 89 "Colón-Aeropuerto" from the Airport to the "Plaza de Colon" in the city centre, every 15 minutes, approximately. The Price is Euro 2.40. There, you can go to Atocha Station or Chamartin Station, both connecting to Albacete, by using urban buses or Metro.
You can make any enquiry on-line about railway routes, timetables and prices, and even buy the tickets with your credit card in advance in the railway company Renfe web page.