Many students use the trains to get to school. It seems like it is the most commonly used transportation in Madrid. The most interesting thing I noticed about the Metro system is that each stop is named after someone or something historical that contributed to the Spanish culture, both locally and internationally appreciated. The train stops Goya and Paco de Lucía are named in the honor of two very famous Spanish artists.
Luckily it was not too difficult to learn the train system. I bet you can learn it in a heartbeat, especially if you enjoy recognizing patterns. At first, I felt confused because I am not used to taking the Metro since I have never lived somewhere with a reliable train system or a place that the train is commonly used as a method of transportation. I quickly fell in love with it because it is extremely reliable, fast, and cheap to get around as a student. It costs only twenty Euros a month for unlimited rides. Without a student ID, each trip costs about two Euros.
Above ground, most of the streets in Madrid are small and one-way streets. Two-way streets do not exist in such a small and compact city. Modern developments have forced the city to add major highways, but you still find a lot of narrow streets built with bricks. This has forced the city of Madrid to establish a reliable train system for daily commuters.
Another method of transportation that comes to mind is walking. People in Madrid walk everywhere, again, because of how compact the city is.