How does friction stop a car? I'm unable to understand how friction causes motion in cars and also is responsible for stopping them.
When it starts the impending motion of tyres is in the backward direction that's why friction is in the forward direction and the car starts moving.
But when the car engine turns off, the car stops after some time, but the condition of tyres are the same as in the previous case and friction must be in the forward direction.
 A: It is not the same friction, but rather the friction between the wheels and the breaking pads (and in general between the rotating parts of the car and their supports.)
A: Plenty of energy is dissipated to make a car stop.
Air rolling over the the surface of the car creates a small friction skin where energy is translated, the perpendicular airflow is an opposing force, the gearbox has plenty of energy losses,the brake pads on a car clasping the brake discs dissipate a lot of energy in the form of heat and opposes the rotational force of the wheels spinning.
A: Frictional Force always acts in the opposite direction of Applied force ( acceleration). As we know, Frictional force is a dissipative force, so a system (here is the car) loses energy (kinetic energy) and eventually it comes to rest.
A: 
but the condition of tyres are same as in previous case and friction must be in forward direction

Not the same.  Friction acts in the opposite direction of relative motion.  Imagine the car is driving on a frictionless surface instead of a road.  It's moving at a slowish speed, and although there is no friction, the wheels are rolling without a slip.
If you punch the accelerator, the wheel spins faster.  The bottom of the tire is moving rearward compared to the road.
If you slam on the brakes, the wheel spins slower.  The bottom of the tire is moving forward compared to the road.
Now you do this on a surface with sufficient friction.  The two situations create friction in opposite directions.  In the first case, friction from the road creates a forward force on the car.  In the second case, friction from the road creates a rearward force on the car.
