How does volume contraction in solvent mixing work?
Yes this happens fairly regularly. It is a deviation from ideal behavior associated with the property of partial molar volume.  For an ideal solution, the total volume always equals the summed volumes of the pure components, but ideal behavior neglects several important facts about real molecules, to wit, that they may have different shapes, and may also experience stabilizing or destabilizing interactions with each other.

It's fairly easy to see how molecular shapes and sizes could affect this property. Macroscopic objects experience similar effects.  Suppose I have a bucket "full" of golf balls and a bucket full of sand, if I work carefully, I can pour quite a lot of sand into the bucket of golf balls because the smaller size of the sand grains allows them to fit into the gaps between the golf balls.  Another example: Suppose you have a 10 liter bucket of golf balls and a 10 liter bucket of tiny cubes packed tightly together. If I then try to pour those two buckets into a 20 liter container simultaneously, it almost certainly will not be able to fit all of the balls and cubes, because they will not pack as efficiently in the 20 L container, costing some space.  These are extreme examples, but illustrate one way that different shapes can play a role.

Differences in intermolecular interactions can play an even bigger role.  If you are dissolving salt in water, the individual ions making up the salt crystal can be solvated very efficiently by the polar water molecules, which experience a strong attractive interaction with the ions.  (Recall that the O and H-atoms in water have partial negative and positive charges, respectively.)  This results in the solution having a significantly smaller volume than expected based on the summed volumes of the pure salt and water used to make the solution.  

Partial molar volume is not too hard to measure experimentally. For something like aqueous sodium chloride it can be determined in a fairly straightforward way from precise measurements of the densities of a series of solutions with increasing concentrations.  However it is worth noting that the volume and mass measurements used for the calculation must be very precise, yielding measured densities with 5 or more significant digits.  This requires careful use of volumetric glassware and precision balances, and the temperature of the solutions must be kept constant throughout.

For purposes of demonstrating the qualitative effect, you could just use water and ethanol (or isopropyl alcohol), which also have a significant negative excess volume. (see the first graph on the wikipedia page for partial molar volume for details).  

For comparison you could use mixtures of benzene and toluene, which behave almost ideally with respect to volume effects.