Madrid adds a flat €3.00 supplement every time you enter or leave a metro station at Barajas, on top of the Zone A single and on top of a 10-trip ticket as well. So the metro to the city is €4.50 to €5.00, not the €1.50 advertised on the map. The supplement is charged per airport trip, so a return costs it twice, and it is not charged on the Cercanías train. Tourist travel cards include it.
Madrid metro has gone contactless: every single and 10-trip metro or EMT bus ticket has to be loaded on a Tarjeta Multi, a red card that costs €2.50 and is reusable for ten years. It is free if you buy a tourist travel card. Machines at the airport sell it, but the queues at the T1-T2-T3 station are long at peak, and the card is the reason a €1.50 fare turns into a €4.00 first trip.
Renfe's airport train stops at Aeropuerto T4 and nowhere else — there is no station at T1, T2 or T3. Land at any of those and the Cercanías is not an option: you take the metro, or you ride Aena's free inter-terminal bus across to T4 first, which adds 15 to 20 minutes before your train even leaves. Airlines routinely sell "train to Madrid" as if the airport had one station.
Tarifa 4 is a flat €33 between the airport and anywhere inside the M-30 ring, 24 hours a day, with no supplements allowed — a driver who adds a night charge, a luggage charge or a pre-booking fee inside the ring is wrong. Beyond the M-30 the meter runs on Tarifa 3, which applies a minimum charge for trips under 9 km before switching to the ordinary tariff, so Pozuelo, Alcobendas or San Sebastián de los Reyes cost roughly €45 to €55.
Uber and Cabify are legal at Barajas but must collect from dedicated VTC pick-up points — at Terminal 1 that is level 1 of car park P1, three to six minutes' walk from baggage reclaim, and Cabify has its own bays at T1 and T2. They are not allowed at the taxi rank or the terminal kerb, and the app walks you to the point. Anyone inside the arrivals hall offering to be "your Uber" or "your taxi" is not a licensed VTC car or a rank taxi.