The answer is in the application of Lenz's law.
An emf is induced and if there is a complete electrical circuit an induced current flows in such a direction as to the motion producing the induced current (emf).
For example suppose that you have the north pole of a magnet approaching a coil which is connected to a resistor.
Because there is a changing magnetic flux linked with the coil an emf is induced in the coil and so there will be an induced current in the circuit.
The direction of the induced current will be such as to induce a north pole at the end of the coil towards which the north pole of the magnet is travelling.
So whatever is moving the magnet will have to do work to push the magnet towards the coil as the two north poles repel one another.
It is that work which is done pushing the magnet which is the source of the electrical energy used to drive the induced current around the circuit.
If it had been a south pole which had been induced then no work would be needed to move the north pole of the magnet towards the coil and yet a current would be flowing producing heat in the circuit.
This would contradict the law of conservation of energy and so it is a north pole which is used to induce the current and not a south pole.