I think my OH starts by chopping off the head and flappy bits of the wings, then splits the skin down the middle of the breast and basically takes it off like a babygro (sorry - that's not a very nice image ). Once he gets to the heel (just below the bottom of the thigh meat) he dislocates the joint and removes the feet. It takes only seconds as the skin comes off easily. Oh, you might have to cut a circle around the cloaca when you get to it, just through the skin - no deeper.
To take off the breast meat you need a thin sharp knife as you need to dissect it out a bit. I start with the bird on it's back and slice down each side of the breast bone, and follow where that leads. If you go at it too roughly you can puncture the guts which is messy and risks contaminating the meat. Once the skin is off you need to wrap the joints as they dry out quickly - or put them straight into a wine marinade. If your bird is large, you will also find nuggets of meat on the back, where the wings join.