From the Madrid airport to Atocha station

Have you checked the airport's website (www.aeropuertomadrid-barajas.com/transportation/madrid-airport-bymetro.htm)?

[Edited] It sounds like you have Rick's Spain book, which lays out all the options on page 489. A door-to-door taxi costs about €30. If you arrive at Terminal 4, you also have easy access to the Cercanias train, direct to both Atocha and Chamartin stations. More below, after Nancy's clarification.

Doug,

You may find this recent thread helpful:
https://community.ricksteves.com/travel-forum/spain/how-to-get-from-the-madrid-airport-to-atocha-train-station

As stated above, we took the Cercanias train ( C-1 line) from terminal 4 to Atocha station.

If you will be taking an AVE train from Atocha, your Cercanias train ticket will be free! ;-)

Have a wonderful trip!

A taxi is not the only direct way to get to Atocha! At both T4 and T1 you can catch the Airport Express bus. Its only stops, after leaving the Airport, are Cibeles, and Atocha station. It absolutely does go to Atocha - I took it in May. (Cibeles is where the bus turns to go to the station, so no time lost, and no going out of the way.) It costs 5 euros, and the trip takes about 25 minutes.

Doug, it looks like you and I were both reading/remembering that info too quickly on p. 489. The bus only terminates at Plaza de Cibeles at night between 23:30 - 6:00. The rest of the day, it does go to Atocha.