Either if you want to travel round Spain or if you just intend to go on a few trips round Madrid, train is definitely the most comfortable means of transport, and the one that allows you to see the best scenery.
Madrid's main long distance railway stations are: Atocha and Chamartín. They run both long distance and commuter trains. There are three more stations for commuter trains: Príncipe Pío, Recoletos and Nuevos Ministerios. More info on stations below.

RENFE is the National Railway Company. They run all the railways in Madrid. In their website you can see timetables, prices, destinations...You can also buy your tickets online with their Tiknet service. it is also possible to book your tickets on the Renfe phone below (Contact Renfe). If you want to get them personally you'll have to go to the ticket offices in Chamartín, Atocha, Nuevos Ministerios or Príncipe Pío. In any of them you can get national and international tickets. Offices in Atocha and Chamartín are open everyday, including weekends from 6.30 to 21.00, and those in Príncipe Pío and Nuevos Ministerios from 8.00 to 20.00 Monday to Friday. See below for the location of stations.

CONTACT RENFE:
National information and reserves: 902 24 02 02
International information: 902 24 34 02
e-mail: atencionviajero@renfe.es

Spain Flexi Pass:
This combined ticket exclusive for tourists allows you to travel round Spain by train. You buy a determined number of days in which you can travel (3 to 10) within a month. Commuter and regional trains are free and for long distance journeys you have to pay a supplement which depends on the type of train you take. For more information you can turn to the Interrail page where you can also get the pass. The pass is available too in the ticket offices mentioned above.