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
During uniform circular motion, at every instant you have a velocity perpendicular to the radius (think about this like you just want to go in a straight line and some force makes you do this circular motion), meaning that the direction of your velocity changes. So there must be some acceleration that gives you that velocity component towards the centre:
From this acceleration towards the centre, we conclude that there must be a force that causes this acceleration.
For an observer just standing on the road looking at you, you do not experience any kind of outward force. From their point of view what happens is similar to this:
Just like the ball you want to go in a straight line but when you reach the bottom of the tube the wall of the tube pushes you back, in your case its the car, so you experience the reaction force of the car.