Hi, Bando,
There are actually several ways to get to Atocha station from the airport.
One is the metro, which requires two changes and takes around an hour.
The other is the RENFE cercanias (commuter line), LIne C-1,which takes less than a half hour. In comparing metro to RENFE, you should factor in two things -- the RENFE trains run less frequently than the metro, so there may be more of a wait; and the RENFE trains only leave from T4, and not the older terminal (T1,2,3). The airlines that fly into T4 are Iberia and all its partners, which includes American and British Airways. But I think most other US airlines (e.g., Delta, United, US) land in the older terminal. To get from one terminal to the other requires getting on the free shuttle bus that runs very frequently.
The third option is an airport express bus, which is described in this post:
traveling-to-from-the-camino/topic9474.html
The bus is probably much easier than the metro, because it requires no changes, because it stops in both terminals, and also because there is not the same problem with pickpockets as on the metro. I think all of these options cost somewhere around 2 euros.
A taxi would probably be around 30 euros (?) to Atocha. Good luck with the travel, Laurie