The Metro in Madrid is one of the biggest metro networks in the world, and it is still expanding. The map that I still have from my first visit in 2006, is a bit outdated to say the least. Which is unfortunately also something you can say about the price of a 10 trip ticket, which is the most used one.
In 2006 this would cost you 6,15 Euros, but since the first of January the price has risen to 9,00 Euros. With the price of a single ticket at 1,00 euro the amount you save is not that big anymore. For visitors it might be better to use single tickets, as usualy at the end of the trip you always have a half used ticket left. If you go far away from the center, you might end up at the network of the Metro Norte, Sur or Este. For these networks you usualy need to change trains, but you also need to buy an extra ticket when you leave the station. (1 euro extra).
Normaly you can buy your tickets are the machines that you will find at every station. If you only have big bills (20 or 50 euros), you can better buy your ticket at a desk, so that you don't get a lot of coins back, but note that not every station (or every entrance/exit) has someone at the desk all the time. If you do buy a 10 trip ticket, note that you can sometimes see the number of trips (viajes) left, when you put your card in the machine to open the doors. If you can't you can simply count the numbers of stamps on the back of your card.
The maps that you can grap in the metro are schematic, which means they are not a very good help to find you way in the city, or even to give an indication if stations are close together. A good example are lines 7 and 5, which split up after stop Pueblo Nuevo, but in reality are still pretty close together for another 4-5 stops. On the map you will also see some figures at some of the station. This is an indication of the time you need when you need to switch lines.
The most used and useful lines for visitors are:
the number 8 line (pink): This is the airport line. If you are coming in by plane, you will have to use this line, if you want to go to the center by metro. The stops are the airport are at Terminal 4, and Terminal 2. To get to the Metrostation at the airport, you need to pay a surplus of 1 euro, and the price of 1 euro for the normal ticket. For most people it is best to head to the end of this line at Nuevos Ministerios. If you are heading for the area around Ventas and Diego de Leon, you can switch lines at Mar de Christal to line 4 (brown). If you stay east of the Retiro Park (around Ibiza), you can switch at Colombia to line 6 (purple).
the number 10 line (dark blue), is useful of you arrive at Nuevos Ministerios and you need to go to the city center. There are a number of stations where you can get out, or switch to other lines. At Alonso Martinez, you can switch to number 5 (green), to go to Chueca, Gran Via, Callao and Opera (all close to the city center.). At Tribunal you can switch to the number 1 line (light blue), which goes to Gran Via, Sol, Tirso de Molina, and the trainstation at Atocha. If you are heading for Callao, Sol or Lavapies, you can also switch to the number 3 line at Plaza de España. On the number 10 line, you will also find the metrostop Santiago Bernabeu, which is outside of the Stadium of Real Madrid and metrostop Lago is in the Casa de Campo, the big park and a nice place to relax in summer.
the number 1 line (light blue) runs from north to south through the center, connecting at Sol to the lines 2 and 3. This line also connects the trainstations of Chamartin in the north, with Atocha in the south. You can also use this lie, with a switch at Pacifico, (to the number 6, grey) to arrive a the big busstation at Mendez Alvaro.
The number 2 line is useful if you want to visit the bullfighting arena at Ventas (the stop is in front of the arena) or go shopping in the Salamanca district. There is also a stop at the north entrance of the Retiro Park (called Retiro) and at the Plaza de Cibeles (Banco de España)
The other lines will not be used very often by visitors.
Do's and Don'ts
The metro can be a very crowded place, and this is also the hunting ground for many thiefs. Be careful not to show off expensive stuff, and than put them in your bag. If you don't want to look like a tourist, memorize the way the metro goes. At the entrance you will find big plates with all the stations, one for each directions. Make sure you don't have to study these boards, as that is a clear sign, you are not familiar with the metro, and therefor most likely a tourist or a visitor from out of town.
In the morning between 7.30 and 9.30 the metro is a very crowded place, as many Madrileños are getting to their jobs. In summer the trains are airconditioned, but you might find a wagon in which the airco is not functioning. Be smart and change wagons, at one of the stops.