Build a better snowflake, and the world will shovel a path to your door.  --KGL

   The simplest technique for growing snow crystals is to allow the crystals to fall freely in a cold chamber.  The images at right show a sketch of such a chamber, and few sample crystals growth with this method [1].  Many additional images can be found in Free-falling Snow.
   Since cold air is denser than warm air, the air in the cold chamber doesn't mix much with the outside air, even with the top cover removed.  To supersaturate the air one needs only to breathe into the box, or use a humidifier, to produce a dense fog.  Within this cloud the water vapor pressure is then roughly equal to the water saturation pressure, which is supersaturated about 5-15 percent relative to the ice saturation vapor pressure (see Ice Properties).  The droplets do not spontaneously freeze until the temperature approaches -40 C, so ice crystals must be nucleated in the cloud.  Various smokes will provide suitable nucleation sites, and dropping a small pellet of dry ice (which cools the air right around it to -60 C) will also produce a fine cloud of sparkling ice crystals.
   The tiny ice crystals grow rapidly in the supersaturated air, and fall very slowly since their terminal velocity in air is low.  As they grow larger, they fall faster, and typically reach the chamber floor no larger than 0.1 mm.  Large numbers of crystals can be formed in this way.  In spite of their small size, with a good microscope a wide variety of morphologies can be observed using this simple technique.

   A variation on the free-fall technique is to use a moving column of air, adjusting the air flow speed to equal the crystal's terminal velocity, so that it remains suspended as it grows [2]. By using a tapered column the resulting air flow tends to stabilize the crystals in the horizontal direction. This technique provides a very close match to natural snowfall, and growth times of up to 30 minutes have been demonstrated.  Since a growing crystal exhibits substantial random motion in the moving airstream, each crystal must be removed from the growth chamber for observation.   Not surprisingly, snow crystals grown using this technique bear an excellent resemblance to natural snow crystals.

  A number of workers studying snow crystal growth have made observations of crystals grown on a substrate.  Although the substrate definitely perturbs the growth to some extent, the effects are not too bad if the supersaturation is low and the substrate is clean.  In this case crystals will not spontaneously nucleate on the substrate, and thus isolated samples can be observed.
   Some of the best pictures were obtained by Gonda and coworkers [4], who developed a technique by which snow crystals are grown directly on a sapphire window.  Supersaturated air is produced in a growth chamber, and silver iodide smoke is introduced to nucleate the production of snow crystals.  The crystals grow for a bit while suspended in the air, then fall onto the window, where further growth can be photographed.  The technique clearly produces nice symmetrical snow crystals (see the examples below), which can be observed using a microscope objective positioned directly underneath the substrate for high-resolution imaging.  The technique seems to work best for plate-like crystals and low supersaturations, where the perturbations from the substrate are minimal.

Above are samples of snow crystals grown on a substrate, published by T. Gonda and coworkers in the Journal of Crystal Growth [4].

  A novel approach to producing artificial snow crystals is to levitate the growing crystals in an electrodynamic trap (a Paul-type ion trap). Such a scheme produces isolated single crystals, since the levitated crystal doesn't touch anything directly.  Growing large crystals using this technique is difficult, however, since as the weight of the crystal increases it quickly becomes too heavy to support in the trap.  Electrodynamic traps for ice crystal growth were first demonstrated by B. Swanson and collaborators [5], and more on this subject can be found at the Ice Particle Microphysics Laboratory.

  Nearly all the work on snow crystal growth done to date has been under normal atmospheric conditions, i.e. with standard atmospheric pressure and standard atmospheric constituents.  Growth under different background pressures and in different gases has been realized, however, and with interesting results.  Under higher pressures, for example, the diffusion constant decreases, leading to "enhanced" growth morphologies -- thinner plates and longer needles than occur under normal conditions.  There is also evidence that the kinetic growth coefficients depend on background gas.
   Finally, a number of workers (including the author) have found that trace chemical impurities in the background air can greatly affect snow crystal growth, a topic which has not been well studied to date.