When the sample is warm and the electrons are not "paired up", it is easy to place the magnet on the surface. Doing so causes the magnetic field from the magnet to penetrate into the sample. Then the sample is cooled and the electrons undergo the phase change.
If the sample was a perfect conductor, nothing at all should happen. This is due to the fact that conductors do not like any form of change in magnetic fields. So where the magnet sits it should sit forever.
But the superconductor will actually manage to remove the now present magnetic field from its interior. It accomplishes this by spontaneously running electric currents on the surface where no currents existed a moment before. The direction of the currents will be such as to create an opposing magnetic field to cancel the one present. As a result, the magnetic field coming from the sample will interact with that of the permanent magnet creating enough repulsion force to levitate the magnet again. The effect is shown in the frame below. If you look closely you can see Liquid Oxygen creeping up over the sample as its temperature drops. The oxygen is condensing out of the air as the sample temperature drops below about 85 K.