Are you talking about the hide or meat? Either way get the hide off as clean as possible. Take your time don't get in a hurry bear are very thin skinned. Try to get as much fat and meat of the hide when you skin it you will have less work later. If you know how to get the feet out it do it if not just separate the joints and leave the feet for the taxidermist. Work the skull out be very careful around the eyes they are near imposable to fix if you bugger them up. If you are going to keep the meat get the bear opened up and cooled as soon as you get the hide off you should get the fat off the meat this will help it to cool and keep it from getting gamey. i the weather is warm rub the meat down good with pepper before you bag it this will help to keep the flys off . Hang the bags where they will get a lot of air, if you throw the bags in a pile they will not cool properly and spoil.
The Alaska Dept of Fish & Game has page of skinning bears their site is down right now but you can check later.
As far as gutting a bear, it is the same as gutting a deer. However you need to get the bear skinned as soon as possible to prevent hair slippage and meat spoilage. Chuck-in-alaska 's post is right on the money.
We all take every precaution when we are hunting and harvesting our animal. Well, what about after the animal is down? Do we know what has happened to that animal over it's lifetime? The following is an example of why we should be careful when we cut.
2 years ago, my father shot a nice 8 point on opening morning of the rifle season in Vermont. It was a beautiful, 2 1/2 year old deer, looked really healthy and moved normally. When my father went to skin it for...