Check out the requirements for entering Spanish territory at link, specially the list of countries whose citizens are required to obtain a visa.
Timetables, prices and tickets at Renfe. The main train station is Madrid Puerta de Atocha. Long distance tickets include a code to get a free commuter train ticket for the same day of the main journey trough the self service machines.
FLIGHTS
TO GET TO/FROM THE AIRPORT
See transports section enlace at:
Station: Terminal 4.
Frecuency: Every 30 minutes
Line: C1
Duration: 11 minutes (to Chamartín station) – 30 minutes (to Atocha station)
Cost: 2,60 eur
Stations: At terminal T1-T2-T3 and another one at terminal T4.
Line: Nuevos Ministerios (in the heart of Madrid)-Aeropuerto.
Cost: 5 euros aprox. (3 euros corresponds to the airport surcharge and the rest is for the regular ticket: 1,5 y 2 euros according to the number of stations to your destination).
Stops: Terminal T1/T2/T4 Departures and Arrivals, O’Donnell st., Cibeles roundabout and Atocha station (6:00-23:30)
Line: Autobús Exprés Aeropuerto 203 (de 6:00 a 23:30) / N27 (23:30-6:00).
Duration: 30 minutes (from Atocha station to Terminal T1, 5 extra minutes up to T2 and 5 more up to T4).
Frecuency: every20 minutes (6:00-23:30) and every 35 minutes (23:30-6:00).
Cost: 5€
Duration: 25-40 minutes.
Cost: 30 € (flat rate to destinations within fija roundabout road M-30).
More info:
Apps to order a taxi operating in Madrid:
Check the best option to move around using Google Maps.
Oficial taxis are white with a red ribbon on the front door and a green light on top, indicating that the it is avaliable. Most of the taxis can take up to 4 passengers but some can take up to 6. If you need the latter, it is better to book it in advance on the phone.
Cost:
More info:
Apps to order a taxi operating in Madrid: