From the airport
Taxi: It's a 20-30 minutes trip and is around €30.
Aerobus shuttle: Drops off at Atocha Atocha, Cibeles (night) and O'Donell-Doctor Esquerdo to Airport T1,T2 and T4 and costs 5€. Bus: Line 200 to Av America, then metro L7 to Alonso Cano. It's a 50 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.
From the airport, take the metro (subway). There are three ways of getting to the hotel. The closest station is "Alonso Cano" (Line 7), this requires that you change twice from the airport and then walk 100 m to the hotel. The second option is to get off the metro at the "Gregorio Marañon" station (Line 10) which requires one change and a 400 m walk. The third option is the "Nuevos Ministerios" station (Line 8) which is direct but requires an 800 m walk.