There is a process for learning these concepts! Typically it involves the old magnet and iron filings. This helps show the shape of the magnetic field, and illustrates magnetic flux lines ( noting that lines of flux is really more of an analogy than reality)... anyway, we can now visualize the magnetic field. We "play with other magnets, magnetic items, and see how the field reacts.
Next we often see the compass type experiment, where we pulse current through a wire near a compass and see the compass needle deflect, demonstrating that current in the wire creates a magnetic field ( Amperes law) AND that the magnetic field can apply a force on the compass needle. By arranging the compass and wire differently we can change the type of deflection (reaction - magnitude and direction) of the needle. Additionally it needs to be noted that the same force ( well equal an opposite) is applied the the wire - according to Newton's 3rd.
As our physics education continues - we perhaps have a small coil and magnet, with the coil connected to a galvanometer ( very sensitive current meter) - we see that we can create a current by passing the magnet through, or by the coils.
We may build a small dc motor / generator, with with we see, and demonstrate a machine, utilizing these concepts to turn electrical current into mechanical motion ( motor) or mechanical motion into electrical current (generator) - etc.
In the end we see or know that a conductor in a varying magnetic field will have a current induced in it, and visa-versa. The filed can vary in essentially any manner, the magnet and conductor moving relative to one another, the mag field could be created by another electrical circuit (conductor or coil) and be expanding or collapsing as the current is changing in that conductor, or the magnetic field could be affected by the "movement" of a magnetic material, or even another conductor in the area. But the core concept is that the relationship of the field and the conductor must be changing.