The direction of the current induced in a conductor by a changing magnetic field is in the direction that establishes a new magnetic field that opposes the direction of the first.
Recall that Faraday's laws of electromagnetic induction are:
Lenz's law says that when a changing magnetic field, like one that is due to a moving magnet, induces an electric current in a nearby conductor, the direction of the magnetic field produced by that current will be opposed to the original changing magnetic field.
Lenz's law is a qualitative law. That is, it doesn't tell us anything about the quantity (strength) of any of the fields, just their relative directions.
The example below is a nice example of Lenz's law behavior, and can easily be done in the lab or classroom.
A permanent magnet, north pole on bottom and south on top in this illustration, is dropped into a copper pipe. Copper is a good electrical conductor, but it is neither magnetic nor paramagnetic.
As the magnet moves, the copper experiences a changing magnetic field, which produces a cirulating current (called an eddy current) in the pipe – as though it were a coil of wire. The direction of that current is, alccording to Lenz's law, such that a magnetic field is induced in the nearby region of the pipe, a field that opposes the direction of the field of the magnet.
As the magnet travels through the pipe, the gravitational force pulling it downward retards (slows down) its motion, causing it to fall more slowly than we'd expect.
The same would be true if the magnet were dropped south-pole downward. The induced current would be reversed, creating an induced magnetic field in the pipe that would still oppose the field of the magnet, just like Lenz's law predicts.
Notice that the opposing magnetic force also opposes the force of gravity in this situation. Notice also that the induced field can never be strong enough to arrest the motion of the falling magnet because that would eliminate the change in the magnetic field experienced by the copper, removing the upward force.
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