From the airport
Taxi: It's a 20-30 minutes trip and is around €30.
Aerobus shuttle: Drops off at the hotel to the airport from 6:00 to 00:30 or at Atocha, Cibeles (night) and O'Donell-Doctor Esquerdo to Airport T1,T2 and T4 (costs 5€).
Bus: Line 101 to Av de American (Ciudad Pegaso stop). It's a 32 minutes trip.
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.