Lenz's Law states that the direction of the induced e.m.f is such that its magnetic effect always oppose the change producing.
Let's say a North pole of a magnet is approaching a coil. The direction of the induced e.m.f is such that a north pole is created at the end of the coil facing the magnet. This will cause the magnet to be repelled, thereby opposing the motion of the magnet. However, when the magnet is moved away from the coil, a south pole is produced to attract the magnet back.
Lenz's law is an example of the principle of conservation of energy. Work must be done to move the magnet against the repulsion or attraction of the induced magnetic poles in the coil. This work is then converted to electrical energy in the form of induced e.m.f.
Another method to determine the direction of the induced e.m.f is by using Fleming's right-hand rule. This rule is usually applied for straight conductors cutting through a magnetic field.