From the airport
Taxi: It's a 20-30 minutes trip and is around €30.
Aerobus shuttle: Drops off at Atocha, Cibeles (night) and O'Donell-Doctor Esquerdo to Airport T1,T2 and T4 and costs 5€. Bus: line 200 to Av America stop every 20 minutes.
Metro: go to the Avenida de América station (changing at Mar de Cristal). If you are in the city for a few days buy a T-10, Multi-person card for 10 journeys, (€12,20). It works on the bus too.