How do I photograph jewelry while being worn?

The diamonds need hard specular lighting to bring out their color/fire, and softer flatter lighting to bring out their brilliance (whiteness/clarity); and the lighting sources will probably need to come from differing directions.

Having the control required to separate the hard lighting for the ring from the soft lighting for the hand is likely to be very difficult. Your best solution may be to composite two separate images using the two types of lighting.

A two-part answer.

1. First, to fix the image you posted simply use a gamma curve. You can use it either using curves or using the level menu.

I am not using Ps here but the result is the same. The difference in using gamma vs other types of curves is that gamma very quickly brightens the dark area (red) but it is gentle with the highlights (green) so the highlights are not blown out.

I am not making additional adjustments like black or white point, so you can see the effect of gamma alone.

2. But for the second part, you need to study how to light jewelry. You need contrast in the surrounding area. You do not use a flat light, you use directionality.

Soft light and dark zones. You need contrast on the illumination.

Product photography is a meticulous matter. The more you dig into it, the more finesse you will discover. To provide some more generic solution, here are three different approaches:

1. In camera as far as it gets: Try to perfectly light the situation. This is only an option in studio as it will take a while and is probably not feasible when a human hand is involved. You can use a variety of lights and flags (shades to keep light away from certain spots) to create the perfect lighting environment. A lot of product photography works like this.

2. HDR: What you want is basically a classic HDR image. You want detail in very bright areas and in more dimly lit areas. Usually this is done via taking multiple images and then combining them in post production. One or more images image exposed for the sparkle and highlights of the ring and one with the exposure for the hand. Then you layer on top of each other and use a layer mask to reveal the elements of each layer that you want to show.

3. Fix it in post: Expose for the highlight and try to fix everything in post production. Problem is, that jewelry needs some sparkle which is achieved with directional (hard) light. Hands however look best with softer light. So you will have to test, if you can use a light that is somewhere in the middle ground and then try how far this will take you. In post you would basically try to raise the lights of the ring to the point where it looks ok, then mask out the ring and bring up the exposure for the hand. You then will need to fix the contrast of the hand as might look grayish by adding contrast.