As I mentioned in my introduction, the best way to get around Madrid is by walking. When the distance is too far to walk, the metro and bus system are a wonderful alternative. A single, one-way metro ticket costs about €1.50. If you are going to be taking the metro more than 4 times during your stay in Madrid, it definitely makes sense to buy a ten-trip ticket. The ten-trip ticket costs €12. You can use the ticket ten times until it expires.
If you are going to be in Madrid for more than three weeks, an abono card may be a good option for transportation. The abono card is a monthly card that gives full access to all Madrid public transportation (city buses and metro lines). For people aged 7 to 25, the card costs €35. The only catch is that you have to apply for the card. You need to have a photo, an application document and your passport to apply for the card. For more information, please visit this website. It gives a great overview of what you need to know about the card.
If you want to use the metro to come back from a night of partying, you may be out of luck. The metro closes at 1:30 a.m. and doesn’t open again until 6 a.m. Unless you are looking to stay out until 6 a.m., a taxi or a long walk is going to be your best way home between those hours. There are some night busses that run from 11:30 p.m. to 5 a.m., but the routes are selective and may not get you where you need to go.
For information about taxis, please visit this tripadvisor article. The article outlines taxi pricing and policies. While taxis are more expensive, they are very convenient. There are taxi stands at many main locations throughout the city and there are always taxis running through the streets.