I would try make one of these light boxes (first tutorial I found just to explain myself - [link]) - the white makes light reflect all over nicely and ensures everything is well lit but not as harsh as a flash. Never made one myself, but I do eventually plan to get down to it one time.
When I photograph my glass beaded jewellery I make sure I am in front of a window in the best part of the day for light, so say noon. This means no bulbs are needed which can make things look yellowey. I don't use flash because this makes the jewellery look odd and the colours slightly inaccurate. Just make sure your aperture and shutter speed are correct for the light and they won't be blurry. Doing it at the right time of day means you will have enough light for the photo anyway. Hope this helps!
According to DPReview, your camera has a hotshoe, which means that if you wanted to spend a bit of money, you could do something like this. You wouldn’t necessarily need professional gear like I used; a hot-shoe-mounted speed light (any brand or make would do in a pinch), a set of inexpensive radio triggers with a receiver that attaches to the flash’s shoe mount, a small softbox or some sort of scrim (basically just a frame with a sheet of translucent white material stretched over it) and possibly a lightstand with a flash mount.
If you go the hot light route, as ~Rcooper and `FallisPhoto suggest, you’ll need a tripod to compensate for the longer exposure times required, and remember to set your white balance for tungsten to compensate for the yellow colour of the lights.
The most important aspect is to get the light(s) in a good place where they will illuminate the jewelry without creating harsh reflections (with the possible exception of facets that you want to be bright). I find that having the lights at about 75º to 90º off the camera axis (either left, right or above the subject) is a good place to start. Side or top lighting will accentuate shape and texture, and will shine through translucent materials and create nice refracted glows. If you’re photographing on white, that will also help bounce the light around and fill in some of the shadow side of the piece, but you may still want to use a reflector card opposite the light if the shadows seem too deep. Salt to taste, as they say.
The link you provided does not take you to a lighting setup. It goes to a piece of shell jewelery that was photographed using a strobe on a boom arm, which has nothing to do with a hot shoe.
"... you’ll need a tripod to compensate for the longer exposure times required ..."
Hot lights don't require longer exposure times than strobes. Hot lights are always on and strobes are on only when the shutter is open. That's pretty much the only difference. You can get 1000-watt or 5000-watt hot lights, if you really want to. That would literally sear your retinas though, so a decent 250-watt setup would probably be all he'd need for something like this, and it whould give him enough light to get away with a 1/250 second or 1/500 second shutter speed. Besides, part of his problem is due to too much light reflecting from the subject. More light is not the solution.
"... The most important aspect is to get the light(s) in a good place where they will illuminate the jewelry without creating harsh reflections (with the possible exception of facets that you want to be bright)."
Exactly! That's why hot lights have an advantage. You will be able to see through your viewfinder exactly what you are going to get and it will save you loads of time setting it up, compared to strobes, which will require you to shoot lots of test photos to see what you will get.
The shot I linked to was one I did recently; I did my best to describe the setup, but if you think it requires a lighting diagram, I can certainly put one up. It has everything to do with the hot shoe on the OP’s camera if she wants to trigger a flash using a radio trigger, since I don’t recall seeing mention of a PC sync port in the specs for that model of camera.
There is a huge difference between hot lights and strobes. Strobes are rated in watts per second. Hot lights are rated in watts per hour.
Shooting a scene with two red-heads, I noticed I needed an exposure time of 1/10" @ f/11, vs. 1/125" (my camera’s max. sync speed) with a moderately powerful strobe. Admittedly, I was using my base ISO of 50, so she could do 1/45" @ ISO 200, and if she were to open up to, say, f/5.6, she could push it to 1/180". But that’s with 1000 watts of light. To get into the 1/250" or 1/500" range, you’d need to crank your ISO up to between 400 and 1000, or be able to open your aperture up to f/1.4 or thereabouts. Most folks just starting out aren’t likely to be using more than 100-watt bulbs. Yes, a 250-watt setup would work (heck, a 60-watt setup would work if you kept the shutter open long enough and didn’t have any other ambient sources), but you still need a tripod.
And yeah, I certainly won’t dispute the need to actually see what’s going on with the reflections in real time. Either hot lights or strobes with modelling lights are invaluable for that, so in that sense I suppose my suggestion of using a speed light is less than ideal.
Are you the one with the recently restored Argus model E TLR that has a flap missing from the top? If so, I found a parts camera in storage yesterday and took the top off. It has all its flaps. Do you want it?
Flashes are probably a bad idea for photographing jewelry or other shiney stuff; I'd use hot lights (tungsten lights that are always on, like in *rcooper102's suggestion). You can see what you are going to get through your viewfinder and make adjustments until you like it, then shoot. You might also consider using a circular polarizing filter to reduce glare. You'll probably want a few catch lights, but nothing overwelming like you are getting. This is a professional copy table: [link] I am not suggesting that you get this exact setup, but it is what some pros use to photograph oil and acrylic paintings, glossy photos, and other shiney objects. Other pros use different setups, but they all have hot lights that you can move around the camera, adjusting distance and angle until you can get it where you want it. You will also probably want to use the fastest shutter speed you can and still get a good exposure.