The battery provides the initial electrical charge needed to start the engine. Once the engine is running the car's alternator generates all the further electricity needed which keeps the car running and also recharges the battery.
Most cars, especially older models, produce a considerable excess of electricity when the engine is running. Some people add a water hydrolyzer to their electrical system to produce Hydrogen gas with the excess electricity. This gas then gets fed into the fuel supply and so increases efficiency. Info on the water hydrolyzer is here:
