I do skin a lot of deer for my customers.  It costs ten dollars, but you can do it yourself.  
Skinning a deer is easy with a little know how and the right tools.  Its always best to skin the deer the same day it was shot.  The meat tastes much better when the hide is removed and the meat is cooled.  It is also much easier to skin shortly after it was shot.  
 My Dad was butcher, I grew up in his little shop, learning to keep meat cool and clean.  I always begin skinning the hind legs first then cutting them off above the hock.  This means there will be no hair filtering down on the meat.  
As you skin the deer the important cuts are splitting the front legs.  Study the photos, watching carefully how the knife follows the line where the brown and white hairs meet.  Stay above the armpit and leave the hide in one piece.  This will allow the taxidermist to give you a fine mount. 

Here I am using a boat winch to hoist up the deer.  It saves a lot of work!

Here I am cutting off the tail.  There is a cartilage near the body that is easy to cut through. 

Now  I begin the cut to split the front legs.  I will follow the line where the brown and white hairs meet to the elbow and then go above the armpit and to the gut incision.  

After making those cuts the hide is simply peeled down as close to the head as you wish to go and the head is removed. 

I have found it much easier to cut the deer in half after it is skinned.   I first cut suitcase handles in the rib cage, then bag the chest and cut it off.  

After loading the front half in the customers car I lower the hind quarters and bag them and carry them out to the car.