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The free thing is for everyday commuters, not for long distance trains.
That said, I would recommend booking in advance , I had to pay over 100€ because everything was full two weeks before muy journey.
If you are taking the train to the North of Spain, you'll be looking for Chamartín Station. There is a pretty good subway network that connects it with the airport. That will be the cheapest way to make it. Just follow the subway map and make sure to buy something called "tarjeta multi" and...
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