Lenz's Law
If you move a magnet towards a coil of wire, you induce a voltage in the coil. A current flows as if there is a battery. If you move the magnet away from the coil, the current flows in the opposite direction. Exactly which way does the current flow in the coil?
On the left of this picture, a coil of wire is connected to a resistor. If the magnet is moved towards the coil, does the current flow right or left through the resistor?
The answer comes from Lenz's law.
Lenz's law that if the magnet moves towards the coil, then they must repel. If the magnet moves away from the coil, they must attract. The coil will always oppose the motion of the magnet.
This is because of the conservation of energy. Suppose that the coil attracts the magnet when the magnet moves towards the coil. Then you do not have to push the magnet. The coil will do it and you get electric current created in the coil without doing any work. This is creating energy out of nothing, which is not possible. This is why the field from the coil must repel the magnet so that you have to work to push the magnet to the coil. It is the work you do that gets converted to the electrical energy of the current.
Lenz's law is usually given in a more abstract form: "The induced current will always be in such a direction as to oppose the change producing it."
Just remember - the current must produce a field that repels the magnet if it moves to the coil, and attracts it if it moves away. Once you know this, you can use the right hand thumb rule to find the direction of the current.