First of all, it's important to realize that, when you photograph a reflective object, you're actually photographing the surrounding scenery as it reflects off the object. This means that it's not enough to just set the object in a lightbox and maybe point some spot lights at it, at least unless you want to make the reflections rather simple and dull.
Instead, what you want, to give the reflections contrast and "sparkle" (not actual sparkle, defined as small spots bright enough to produce visible flaring in the photo, but just the appearance of glitter) is to surround the object with high-contrast scenery that produces the appropriate look when reflected off the object. (Of course, you usually need to leave some neutral background behind the object, but this need not be a large area, especially if you use a long lens.) This is as much an art as science, but here are a few things to try:
Add high-contrast edges to the background. If you're using a lightbox, try covering parts of the inside of the box with black cloth / plastic / cardboard, or with colored translucent paper or plastic.
Add gradients to the background. When reflected off a faceted object, each facet will reflect a small part of the gradient, giving both contrast between facets and subtle color gradations within each facets.
Choose the colors in the background to give the effect you want. With a reflective object, the colors you see in the photo depend as much on the surroundings as on the object itself, so you can "paint" the object by choosing the appropriate background.
Use or mimic natural backgrounds, as these often have color schemes and patterns that, even when scrambled by reflection, evoke desirable feelings in the viewer. Even if you go for a purely abstract background, it's often a good idea to e.g. keep the darker areas of the surroundings in the bottom half, and the lighter areas in the top half, as our brains have evolved to expect such an arrangement and find it natural.
As for actual sparkles, these are formed when a small fraction of the facets in the object reflect something so bright that it saturates the camera (or the eye) and creates flares. If your object has enough small facets, just pointing a single bright light source at it will indeed produce sparkles. If not, you may need to use multiple small point lights (such as LEDs, halogen lights or small mirror reflectors pointed at the object) to obtain more sparkles.
One trick you can use is to fix the object and the camera in place, and then move the point lights around until you get nice sparkles from each of them. For a more natural-looking result, you may also want to preferentially place the sparkle sources in "natural" locations, such as in the lighter parts of the surroundings or near the main light source.
Also note that the appearance of the sparkles will strongly depend on your camera and lens. For pretty "starburst" sparkles, you'll probably want to use a narrow aperture and/or a cross-screen ("star") filter. This page from SLR Lounge shows some nice examples of the effect of aperture on sparkles in photos:
(Image from SLR Lounge, used under the CC-By-ND 3.0 license.)
Finally, note that dynamic range is very important here. The notable thing about sparkles is that they're much brighter than the rest of the object. You can't really reproduce the true intensity of the sparkles on screen (or on paper), even if your camera could record it in the first place, so you have to find ways to give the impression of brightness without the actual brightness.
Starbursts are one way of achieving this; so is the use of a dark reflective surface, as you've done, as it effectively gives the viewer two pictures of the object, taken with different exposures, that the brain can combine to reconstruct more of the dynamic range you'd see if you were looking at the object directly.
Ps. I wrote most of the above before you posted your example photo. Having seen it, my specific suggestions would be to:
- Keep the black acrylic — it seems to work very nicely for what you're trying to do.
- Step down the lens further, or get a starburst filter for your lens, to add more "sparkle" to your sparkles. (This alone might do the trick for you.)
- With that many facets, you probably don't need too many light sources to get decent sparkles. The non-sparkly parts of the object might benefit from a bit more diffuse lighting, though, possibly with some subtle color to add contrast. Consider replacing some of the black velvet, especially on the left, with lighter colors and/or gradients, and maybe adding some secondary light sources.
- While you're adding some diffuse lighting, consider moving the main light source a bit more off to the side. Right now, most of the sparkles are on facets facing pretty straight into the camera, giving the picture a bit of the unnatural look often associated with excessive use of in-camera flash.