Even though Madrid is large and has a great public transport system, it is a terrific city to explore on foot. All flights arrive at the Barajas International Airport, which has separate national and international terminals. Be careful and be very aware of your belongings. While there is little threat of physical harm, theft is a real issue. Credit cards, cash, and passports should be kept close to the body.
Many people speak some English, but people appreciate any attempt at Spanish.
It's always a good idea to learn a few basic phrases. Castilian is spoken everywhere, in addition to regional dialects like Catalan and Basque. There is no better place than Madrid. The area around Plaza de la Puerta del Sol is hopping from 9 p.m. till the wee hours of the morning. The party really doesn't start until after midnight and it continues until dawn.