A changing magnetic field induces an EMF across a conductor in it, and if the conductor offers a closed circuit then induced current flows through it

The induced EMF in a conductor is directly proportional to the rate of change of the magnetic flux.

In essence, all you need to create a magnetic field is a conductor moving in a magnetic field. Any can move and it's the relative direction that counts. The faster the movement the higher the induced emf and the current.

This process is not "free". When we induce a current in a secondary coil it will also produce a flux which will induce an EMF in the primary coil.

The primary coil induces a voltage, therefore a current in the secondary coil which will in turn induce a voltage and current back in the primary.

There is another type called the self-inductance which will be studied next