I start by cutting off the wings and lower legs. It's important to leave the head attached.
There you have a whole skinned quail.
Next, you pull the leg over the back, and pull the legs off one at a time. It's best to pull from the front to the back.
Here you have a whole quail with the legs and thighs removed and in the pan.
You could see that I had the quail by the head with my right hand. Just pull the head and neck off and the intestines come with it.. You can see that I have the breast in one hand and the head with the backbone and guts in the other hand. Notice that my hands are still clean
I've done them every other way that's known, but this has always worked best for me. I can do them as fast as a helper can clip the wings and feet.