I'm no pro. but here's sorta how I skin when I first started. Once you done a few hundred you seem to perfect a few things. Being a beginner. Don't concern with clean skinning. When skinning more flesh less damage and it can make fleshing sometime easier.
First I cut the feet and tail off. leaving as much of the possible


I cut around the anal area

spit it right up the center from tail to the bottom teeth

then I use a pelting knife an start laying the fur open. About two inch from the center cut you can pickup a layer of flesh. beaver has multiple layers of flesh. I call that safe zone.

I take a sharp small knife skin lower section of the head as shown

I take a screw driver pop the legs threw.

I shave the legs back with the pelt knife

Now I turn the beaver to it's side and work the fur off with my knife

The final is working the head.
After alot of skinning. I sorta half clean skin a beaver all I really have to flesh is around the head and tail area. I can skin a beaver like that in about 8 to 10 min. It use to take about 30 or 40 min. I can skin and flesh one in about 20 min. But it still a pain in the booty. I hope this help you all some. I give free hands on training course in my fur shed.