Arrivals - Departures - Terminals -  Location - Airlines

Metro
The airport is well connected to the Madrid Underground. But metro line 8 doesn't reach the city center, so you will have to connect to other lines. Sol is the city center.

Metro line 8 does terminate at Terminal 4. From there it goes via Barajas to a metro station at terminals 1, 2 and 3 at the Madrid Barajas airport (MAD).

Metro line 8 connect to metro line 4 at Mar de Cristal metro station.
Metro line 4 goes between Mar de Cristal and Av. de America metro station, where it connect to other lines, but continues to Arguelles via Colon.

To reach colon metro station with metro line 4 you need around 40 minutes travelling from the airport. At Colon metro station you are in the area of the Prado museum and a big city park.

Link: http://www.metromadrid.es