I read in a book that when a conductor is placed in an electric field then the free electrons in the conductor will align in such a manner that an electric field is induced which is opposite to the external field and the net field inside is zero. The conductor has innumerable number of electrons that any electric field can be cancelled. Then how does a conductor conduct electricity?
You are misunderstanding. ELECTROSTATIC FIELD inside aconductor is zero, not electric field. ELECTROSTATIC field means the electric field created by charges at rest.
We can understand this property by considering a conducting slab placed in an external field E. We can argue that the electric field inside the conductor must be zero under the assumption that we have electrostatic equilibrium. If the field were not zero, free charges in the conductor would accelerate under the action of the field. This motion of electrons, however, would mean that the conductor is not in electrostatic equilibrium. Thus, the existence of electrostatic equilibrium is consistent only with a zero field in the conductor.
Thus when charges are in motion, it means that there is no ELECTROSTATIC equillibrium, thus ELECTROSTATIC field is nonzero.
Now if we apply a potential difference across a conductor, we have created an electric field inside the conductor. Thus electrostatic equillibrium is disturbed and electrons flow under applied filed, and so does the current
We need to distinguish between the electrostatic case and the case of a conductor which is part of a circuit.
Say you take a length of wire and place it in an electric field so that the wire is parallel to the field. For some short period of time the external field will exist inside the wire and as a result some free electrons in the wire will move in the opposite direction to the external field until the field resulting from this redistribution cancels out the external field inside the wire. After that, no more electrons move.
Where you see a continuous current in a conductor is when it is connected to some sort of current source (battery, photovoltaic cell etc.). Here you are continuously adding electrons to one end of the wire and removing them from the other. This creates an electric field in the conductor. You could think of the resulting current as the electrons as "trying" to redistribute themselves to cancel out this field but their efforts are thwarted by the action of the current source.
PLEASE REFER THE FOLLOWING TEXT: http://ncertbooks.prashanthellina.com/class_12.Physics.PhysicsPartI/Chapter%202.pdf
Inside a conductor, electrostatic field is zero
"Consider a conductor, neutral or charged. There may also be an external electrostatic field. In the static situation, when there is no current inside or on the surface of the conductor, the electric field is zero everywhere inside the conductor. This fact can be taken as the defining property of a conductor. A conductor has free electrons. As long as electric field is not zero, the free charge carriers would experience force and drift. In the static situation, the free charges have so distributed themselves that the electric field is zero everywhere inside. Electrostatic field is zero inside a conductor."