This setup of photographer Caren Harris, at the Asheville Humane Society, shows the setup she uses - apparently one flash with a Gary Fong diffuser and a silver reflector. It appears she's using a 70-200mm lens. Judging by the distance she is from the dog she's probably using a full frame camera which doesn't have the 1.6X multiplication factor making the focal length longer and thus forcing the photographer to stand further away from the subject.
I decided to try a similar setup, using the equipment I had, which included a smaller silver reflector which you'll see in one of the following pictures.
I triggered the flash on my Canon 7D with an STE2 flash trigger in the flashshoe. The 7D will communicate wirelessly with the 580EX II. I have the previous version, which doesn't communicate.
I didn't have a chair, but I like the idea of using one because it limits the amount of traveling the subject can do. Looks like she's used sheets. I pulled some fleecy stuff out of my storage room and I think it may be quilt batting. It worked very well. I clamped it over my canvase background and I suspect it's leaving lots of little nerdles of white stuck to it. See following images for my results.