We've learnt that friction is the opposition of motion and that friction appears the instant a force is applied on an object i.e when an object is at rest (with no force acting on it) then there is no frictional force. The moment a small amount of force is applied, friction becomes a factor. Therefore, friction is just the "equal and opposite" force between two bodies. Now, let an object be accelerated to a velocity 'v'. Then, let the acceleration cease. Ideally, the object will come to a stand still. However, if the acceleration is zero, doesn't that mean that there is no force => there will be no "equal and opposite" force i.e frictional force. And, only if there is an opposing force will there be retardation. Obviously, my reasoning is flawed, if not then an object that has been accelerated to a velocity will continue to move at a constant velocity. However, I don't get where my reasoning is flawed. Please do help...
Sorry, but the currently accepted answer is not precise enough.
In the situation you discussed, there is no applied force acting on the object, but there is still the normal force $N$, which prevents the object from "falling through" the surface due to gravity.
The most common model of kinetic friction is $F_k = \mu N$, where $\mu$ is the coefficient of friction between the interacting surfaces.
Since the object you discussed is in motion and is acted upon by a normal force, it is also acted upon by a friction force. From Newton's third law, the forced paired with this friction force is a friction force of equal magnitude but opposite direction that acts on the surface the object is sliding on. If our surface is as massive as the Earth, we can ignore any effects the paired friction force might have on it.
Remember that when you push the object with an applied force $F_A$, the equal-but-opposite force paired with $F_A$ is not the friction force, but rather the normal force exerted by the object on your hand. The friction in your scenario occurs between the object and the surface it is sliding on, not between the object and your hand.
Friction comes into play whenever there is relative motion between the surfaces in contact or a tendency of motion between the same.There need not necessarily be an externally applied force on either of the bodies,that is,there need not necessarily be a relative acceleration initially,merely relative motion or a tendency for the same. It is the frictional forces that produce this relative acceleration once the necessary conditions of relative motion have been established.