Madrid's Metro is quick, efficient, clean, safe, and cheap, with more than 200 stations on 12 numbered and color-coded lines. The network operates from 6:30 a.m. until 1:30 a.m., and you'll seldom have to wait more than a few minutes for a train. The Metro Madrid Web site is in Spanish, but the plano (map) doesn't require translation, and the self-service ticket machines in the Metro stations are multilingual and easy to use.
The local bus network is run by EMT Madrid. Buses operate from 6 a.m. until midnight.
You can buy a discounted 10-journey Bono from any Metro station or bus information booth, and it--like single-journey transit tickets--can be used for either underground or bus travel. If you plan to travel extensively by Metro or bus, consider buying a Tourist Travel Pass (Abono Transportes Turístico), which permits unlimited travel for 1, 2, 3, 5, or 7 calendar days. (Get the cheaper Zone A version unless you plan extensive suburban travel.)
photoMadridVision buses. These "hop on, hop off" double-deck sightseeing buses operate on two routes: "Historic Madrid" (the city center) and "Modern Madrid" (the neighborhoods north of the center where many upscale chain hotels, office buildings, and shopping malls are located).
TheMadridVision buses won't take you anywhere that you couldn't reach by public transportation--or, in the case of historic Madrid, on foot--but if you're on a tight schedule or want to minimize walking, they can be a good value. (You can ride MadridVision buses free with the Madrid Card; the Madrid Card Cultura provides a 10% discount.)