It may be hard to believe, but a battery-powered electric car worked pretty similarly to the way any other electric device works--just with a much, much bigger battery.
Modern electric cars have a lithium-ion battery pack composed of smaller cells that are grouped into what are called modules. Most electric cars use large-format cells--between 100 and 200 of them--but Tesla electric cars from the Silicon Valley startup take a different approach. They use thousands of much smaller cells, very similar to those in your laptop. Here's the difference, though: Your laptop may use 6 or 9 such cells, while a Tesla uses 5,000 or more.
The battery pack is usually mounted low down in the car, to keep its substantial weight close to the ground. In some cars--the Nissan Leaf and Tesla Model S, for example--it's actually thin and flat, and mounted underneath the passenger compartment.
The battery powers an electric motor that actually turns the driven wheels of the car. There's a differential with a reduction gear, but no transmission, since electric motors can run at a far wider range of speeds than a gasoline engine can. That means no transmission is required to match the engine's speed of peak output to the road speed--which makes electric cars much simpler to engineer.
The electric motor not only powers the car but also converts into a generator to recharge the battery as the car glides or the driver puts on the brakes. Electric cars are far more efficient than gasoline cars, even hybrids, and this so-called regenerative braking can recapture up to one-third of the energy expended to put the car into motion in the first place.
Beside the battery pack and the electric motor, there's a third set of electrical devices, collectively known as the power electronics. These are heavy-duty circuits and other components that change the voltage of the electricity used by different components, and also convert it from Alternating Current (AC) to Direct Current (DC) and vice versa. These include an onboard charger that takes wall current from the charging plug and converts it to the right kind of electricity to recharge the battery pack.
Those three sets of components make up pretty much the entire powertrain of an electric car. There are usually one or more radiators that shed heat from liquid coolant that circulates through the battery, motor, and power electronics to keep them all operating at their best temperature--which will considerably lengthen their life. Like people, electric-car batteries tend to want to stay around 70 degrees Fahrenheit.