Arriving to Madrid, you definitely pass one of two gates of the air: Barajas or Torrejon. Barcelona Barajas international airport is the main airport in the capital. International and domestic flights are available here. The second air hub serves only charters, so you can get there only if you or your company rents the plane.
How to get from Madrid airport, if you don't know Spanish? Book your transfer at GetTransfer.com. Here you do not need knowledge of a foreign language: you can apply in any of the 10 languages.