Friction forces act as a response, and opposite, to velocity, not force (that would be normal forces).
The car has a liner velocity in the forward direction, and it keeps moving indefinitely, ignoring any residual friction. Then, if the steering wheel is turned left, the front tires are rotated to the left, thus there appears a frictional force perpendicular to those tires. This force is caused by the tires resisting the movement, just as any other friction. The interesting thing is that tires can rotate freely only in one direction, but not in the perpendicular. Thus the friction appears only in that non-rotating direction.
This force will point not perpendicular to the car, but perpendicular to the tires. The difference is small, since the actual angle that the tires are rotated is quite small, particularly at high speeds. Also, once the car is rotated from the straight line, a small lateral friction will appear also in the back tires, because the velocity will no longer be aligned with the axis of the tires.
![Force diagram](https://i.stack.imgur.com/LP8EU.png)
There are two types of frictional force, the static friction and kinetic friction.
Kinetic friction is the force experienced when you drag an object on the floor. Static friction is what enables you to hold objects without it slipping away from your fingers.
Similarly, as you drive, assuming that the wheels don't spin, your wheels are pushing backwards against the floor, and friction is the opposing force that pushes your wheel forward, enabling you to drive forward. If static friction does not exist, your wheels will simply spin, and you car will remain stationary, because there is no frictional force to push your car forward. (If you can't visualize this, think of what happens when you row a boat. You push the paddles backward so that the water resistance force pushes your boat forward)
As you negotiate a turn, if you are turning left, your wheels are pushing to the right against the floor. Static friction allows the floor to "push back" against your wheels, allowing you to turn left.
In this case the only force that is acting in the direction of turn(centripetal force) is the frictional force. As the floor is the only surface that is in contact with the car, friction is the only force that is acting on the car towards the centre of the turn, pushing the car towards the centre of the turn.
![enter image description here](https://i.stack.imgur.com/NrWaA.gif)
Best Answer
Frictional force opposes sliding motion, basically. Car tires produce centripetal force by changing their angle relative to the
rest of the car's orientation
. The tires do not slide in the direction of thetires' orientation
: they roll. Friction in this direction rotates the tires, or if the engine is applying force to the wheels during the turn, friction prevents the tires from "burning rubber", and pushes the car in this direction.Meanwhile, motion in the direction of the
rest of the car's orientation
is opposed by friction only to the extent that it is not motion in the direction of thetires' orientation
. The velocity vector corresponding to therest of the car's orientation
can be understood in terms of these two orthogonal components. The component corresponding to thetires' orientation
is basically not subject to friction for our purposes (ignoring whether one's foot is on the gas pedal). The component that does not correspond to that other component is orthogonal and opposed by centripetal friction.If
tires' orientation
$=$rest of the car's orientation
, basically no centripetal friction results.