From the airport
Train: C1 to Nuevos Ministerios then metro L10 to Gregorio Marañón. It's a 30 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.
Taxi: It's a 20-30 minute 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€.
From Barajas Airport, take the metro and get off at the Nuevos Ministerios station. Change metro line here and take line no. 10 to the Gregorio Marañon station which is a two minute walk from the hotel.