Step One: Remove the Front Quarter
With the deer lying on its side, stand behind the shoulder and lift the near front leg. Run your knife blade across the thin skin of the armpit. The front quarter is free-floating (no bone attaches to the skeleton). Separate it by progressively working the knife underneath the leg and shoulder as you pull the leg up and away from the rib cage. Follow the contour around the top of the scapula closely to avoid cutting into the backstrap. (You can reduce your load by skinning and boning the quarters, or just pack them out intact.)
Step Two: Remove the Rear Quarter
Using a slicing motion, insert your knife under the leg to the inside of the scrotum or udder and draw it toward the rear. Slice progressively deeper, making shallow half-moon cuts and working forward to the hip point where the quarter attaches to the spine; and rearward to the near side of the anus, where the blade's downward progress is stopped by the pelvic floor. When the hip joint is exposed, cut through the ligaments at its juncture to free the rear quarter. Keep following bone, feeling with your knife blade, until the rear quarter is detached.
Step Three: Remove the Backstraps
Remove the skin from the upper side of the deer, peeling it back to expose the twin, tubelike muscles that run from the hip point forward to the front of the shoulder. Cut down along the inside of the backbone, then tease the long strip of meat free by working the blade horizontally along the curve of the rib cage. Be careful not to puncture the gut on the rear portion, where there are no ribs to stop the blade.
Step Four: Remove the Tenderloin
The tenderloins lie underneath the backbone, from the last ribs to a point between the hams. Carefully work the knifepoint under the five short spinal processes behind the last rib, then reach up under the spine and tease the tenderloin away from the bone. These muscles are so tender that you can often remove them with your fingers. All that remains is to turn the deer over and repeat steps 1 and 2.