Well first you kill a bear.
I like to do it this way. Others may have different ideas.
I lay the bear on a tarp. If you want a rug:
Slit from heel to heel on the inside of the hind legs.
Slit from heel to heel on the inside of the front legs.
Slit from anus to chin.
Skin out the legs on one side of the beast. Then skin the rest of the same side of the bear.
Flip the skin out of the way.
Cut the hind leg off at the hip joint.[ knife only, go slow.]
Cut the front leg off complete with shoulder. [again you only need a knife.]
Filet the back strap.
Roll the bear over onto the "carved" side and repeat for second side.
Two hinds, two fronts, two backstraps,
one hide.
Now you can cut the paws off when you do the legs, and let the Taxidermist skin the feet for you , or you can spend a little more time skinning before you cut the legs off.
Ditto the head. I like to skin everything and then put plenty of salt on the hide. If you think you have too much salt, that is usually a little less than you need, so add more. There is no such thing as too much salt
After the salt
fold the hide , flesh to flesh loosely. at least once a day open and resalt. DO NOT PUT in a plastic bag. it will sweat and the hair will slip.
Oh yeah! take your watch off before you start. I don't gut them at all.
This method works with deer, elk, moose with a few minor adjustments.
I don't bother with the ribs.