Despite being an enormous city (with over 3 million inhabitants), it’s easy to get around using the public transport system in Madrid. There are buses and trams, as well as an extensive metro network. Transportation costs are pretty reasonable as well, especially if you get a monthly student ticket.
Most will travel to the city by plane, since Madrid Barajas Airport is the largest in Spain, and is fed from major cities across the globe. After landing, you can make the journey via metro, bus, train or taxi.
Metro - €4.50, 15 minutes and terminates at Nuevos Ministerios in the city centre, Line 8.
Bus - €5.40 minute journey with multiple stops in the centre, "Airport Express"
Train - €4.50, 15 minutes and goes to Chamartín, Nuevos Ministerios, Atocha or Príncipe Pío stations. From Terminal 4.
Taxi - €20-25, of course it will take you to your door.
You don’t need to book any transport in advance, and all services run from early morning until late at night. The buses run 24/7, all year, so you can always count on them to get you safely inside the city.
Madrid Atocha Train Station can also be accessed from all over, so if you decide to come by train you won’t be the first. The station is about 2km from the "true" city centre, so you can hop over on the metro, bus or in a taxi if you’ve nowhere else to go. It’s really easy, so relocating by train is very feasible, even with a number of bags!
You can make your way from one end of the city to the other easily using the bus, metro or tram system. There are also trains for going into and around Madrid’s suburban areas. Of course you can walk and cycle around too, but the city is pretty big so public transport can save you a lot of time.
There are city bikes in Madrid - their BiciMadrid service - but it costs money, unlike at many other European cities. There is an annual subscription fee of €15, then €0.50 per 30 minutes you spend on the bike. After the second hour, it’s €4 per hour - pretty expensive really. If you don’t want to cough up for the annual fee, it costs €2 for the first hour and €4 thereafter.