I am trying to do some pretty jewelry photography and I am wondering what type of lens I would need to create a shot like this? Also what is the lighting environment required to take this shot?
You want a macro lens. In both Canon and Nikon lineup there is a 100mm f2.8 macro. Both are excellent. If I remember correctly a 100mm macro is made also by Tamron, Sigma and Zeiss. If you don't have one try a prime lens on an extension ring (the basic 50mm works fine).
On a cropped sensor body a 60mm lens would give you similar view as a 100mm on full frame camera, but the 100mm is still better as it gives you more working distance (it comes at premium when doing macro).
Lighting jewelry is tricky, as it is all shine and sparkle. You want as soft light as possible. A macro tent (the smallest one) helps immensely.
Be careful with your aperture. If you push it too hard (f22 or so) you will run into diffraction artefacts. Best to keep it to f11 or lower and add depth of field via stacking.
A stable tripod is must, and a focusing rail and wire release highly recommended.