As Eduardo suggests, you can take the subway from the airport to "Nuevos Ministerios" and the the commuter train from there to "Atocha". It should take you about 25-30 minutes. Perhaps this is even faster than a taxi.
By the way, if you have the train tickets by the time you arrive at Nuevos Ministerios, I've heard you can travel for free on the commuter trains from Nuevos Ministerios to Atocha just showing them. It seems they are kind enough to let you go for free to your departure station. However, I've never tried myself and I'm not sure whether this system is still valid.
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The best tips from your favourite hostal in Madrid.
Hostal Chelo at
http://www.chelo.com