Two Cases arise:
Case 1: When the conductor is not immersed in an External Electric Field and there is no current flow or rather under electrostatic conditions.
When there is no external electric field the total charge inside the conductor is zero. Hence there is no electric field inside the conductor. If we argue that there are electrons and protons, then we say that the lines of force start at positive charge and end at an equal amount of negative charge. Therefore the electric field exists inside an atom but not outside it. Since the positive and negative charge inside a conductor is equal, we conclude that the field inside a conductor is zero.
Case 2. When the conductor is immersed in an External Electric Field and there is no current flow or rather under electrostatic conditions.
When external electric lines fall on a conductor negative charges flow opposite to the lines of force and accumulate on one side of the conductor and positive charge accumulates on the opposite side of negative charges. These are called induced charges. These induced charges produce an electric field inside the conductor and opposite to the external electric field. The two fields being equal in magnitude and opposite cancel. Therefore the electric field inside a conductor is zero.