The Airport in Barcelona (Aeropuerto Barcelona) is at El Prat, just south west of the city. This Airport contains three Terminal named A,B and C and all of them are equipped well with facilities. You will find a fair amount of exchange cabins, restaurants, tabaccos to by your bus tickets and a tourist information desk.
The airport is connected to a bus service which runs between the terminals and the city center of Barcelona, Placa Catalunya. This bus usually will stop at three further locations of the city center, Placa d'Espanya, Urgell and Placa Universitat. Buses run every 10 to 15 minutes and the trip to downtown Barcelona will take you roughtly 30 to 45 minutes. The travel costs of this bus trip is 3,80 Euro for a single and 6,20 Euro for a return.

All flights to Madrid arrive at the Airport Barajas (Aeropuerto Barajas). This airport is located about 13 km (8 miles) northeast of Madrid's city centre. The airport provides you with four Terminals. Taking a taxi the travel to downtown Madrid from the airport will take you no longer then 20 minutes when the traffic is normal that means no rush hour time.
You even have the option to travel by Metro directly from the Terminals 1 and 2. Simply take the Metro line no. 8 and then change into Metro line no. 10 heading for Madrid's city center at Nuevos Ministerios station.
Last but not least you can always take the Bus from the airport to town. It's the no. 200 which will get you as far as Avenida Americas Metro station, from there you might want to change again heading further downtown.