Theory
The Meissner effect is based on two principles - Lenz's Law and superconductivity. Due to Lenz's law the introduction of a magnetic field will cause "screening currents" at the surface of the superconductor. This effect will levitate a magnet as long as the magnetic field does not exceed the critical magnetic field. A magnet that is suspended by the superconductor has two interesting properties; it does not move, and it can spin without friction. The ability for the magnet to stay perfectly still is due to flux pinning, in which the magnetic field is able to penetrate the superconductor by means of impurities in the crystal structure.
Note that there is a difference between a perfect diamagnet and a superconductor.