If you are flying on Delta, you arrive in the old terminal, which means you have different choices than those who arrive in T4 (Iberia and partners).
1. Take the intra-airport bus to T4 and take the half hour train ride on CercanĂas (the commuter rail line) to Atocha.
2. Take the metro from the old terminal to Atocha. This will require a change in Nuevos Ministerios (which is a huge station with long distances between lines) and takes about a half hour if everything goes well.
3. A bus that seems like a pretty good option, but which I have never taken.
Information about how to go by bus from Adolfo Suárez Madrid-Barajas Airport (MAD) to city centre
www.madrid-airport.com
4. A taxi — 35 € flat fee. In a pinch, this is likely to be the fastest, at least if it’s not high rush hour.
Good luck,
@EL LECHERO!