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€.
Subway: Take L8 from airport to Mar de Cristal. Disembark at the Colombia station. From there you can walk ten minutes to the hotel. (approximately 38 min). If you are in the city for a few days buy a T-10, Multi-person card for 10 journeys, (€12,20). It's cheaper than a single ticket (1,50€).