Quantum superposition can be shown by the double-slit experiment. It was first used to prove that light consists of waves. Today, the experiment is used to help people understand the way that electrons can act like waves and create quantum interference patterns.
For this experiment, a beam of coherent light, such as a laser, is aimed at a barrier with two vertical slits. The light passes through the slits, and the resulting pattern is recorded on a photographic plate. When one slit is covered, the pattern is what would be expected: a single line of light, aligned with whichever slit is open.
Intuitively, one would expect that if both slits are open, the pattern of light will reflect two lines of light aligned with the slits. In fact, what happens is that the photographic plate separates into multiple lines of lightness and darkness in varying degrees.
This shows that the light is acting as waves, and the two waves are interfering with each other, adding together in some places to become brighter and canceling out in other places to become darker. The same pattern is shown if photons or electrons are used.
Where this becomes surprising is if the experiment is repeated so that only single photons or electrons are sent through the two slits, one at a time. The same interference pattern is shown, even though only one particle is present. It is almost as if the one particle goes through both slits at the same time and interferes with itself. In order to do this, it must be in a superposition state.
Interestingly, if a detector is added to determine which slit the particle goes through, the probability wave collapses, and the interference pattern disappears. The loss of the superposition is known as quantum decoherence.