The third rail, on many light rail systems such as subways and elevated trains, is mounted above and to the side of the two rails which support the train's weight.
The third rail is mounted on plastic insulating supports, and is usually covered by a plastic shroud which prevents track workers from accidentally contacting it.
Power is supplied to the trains through the third rail. While the voltage may vary between different systems, it is usually around 800 volts DC. This is supplied by mercury arc or silicon rectifiers off of the AC power grid. As I witnessed once in a rather cool malfunction on Miami's Metrorail system, there is enough current present at the third rail to sustain the arc and melt down the iron rail (estimated failure current in the THOUSANDS of amps) in the event of a short circuit! Ever seen a waterfall of molten iron?
The two other rails used in a third-rail system are connected to both earth ground and neutral on the power system, and serve as a return path for the power used by the train. Sometimes, third rail and overhead wire systems may be combined. Power is picked up from the third rail by a sliding metal contact on the side of the train cars, which sort of resembles a duck's foot. The sliding action of the contact on the third rail probably helps keep the iron contact surface from rusting and thus becoming less conductive.
The third rail system is not without its problems. First, it allows unauthorized, or, authorized persons walking the track to come in contact with the 800 volt DC source, with expectedly catastrophic results. Second, the contact on the side of the train can sometimes get borked up, leading to truly awesome fireworks. Watch for it when riding at night or in a tunnel!