The clean and highly efficient metro is by far the quickest way of getting around Madrid, serving most places you're likely to want to get to. Lines are color-coded, and the direction of travel is indicated by the name of the station. It runs from 6am until 2am and service is frequent:
Morning rush hours every 2-3 minutes, daytime every 4-6 minutes, every 15 minutes after midnight.
FARES (2006, for zone A - Madrid City)
Single ticket (no transfer between metro and buses) - €1.00
Metrobús (10 rides (bono de diez viajes), no transfer between metro and buses) - €6.70
Daily passes for a day or more are also available -- just ask for a "Abono transporte turístico".
Note that some stations or sections may be subject to periodic closures as a result of the modernization and extension program which is currently underway,
but the good news is that many of the older trains are being replaced with extremely modern trains and expanded platforms.
Here is a PDF map of the system or you often can get one (plano del metro) at any station.