1-60 Skinning Guide
Visit any Skinning Trainer, and learn Skinning Apprentice.
Don't forget to buy a Skinning Knife, it gives you +10 Skinning skill.
Beasts in the immediate starting area can't be skinned because that area is for level 1-6 players and you won't have any profession until you reach level 5.
When you reach 60, visit your trainer and learn the next rank of Skinning.
60-110 Skinning Guide
Do not leave these zones until you reach 110!
110-185 Skinning Guide
When you reach 150, you will have to visit your trainer.
185-205 Skinning Guide
Visit your trainer as soon as you reach 205. You could probably leave the zones at 200, but there will be a few mobs that are level 41 in Thousand Needles and you need a Skinning skill of 205 to skin a level 41 mob.
205-265 Skinning Guide
265-300 Skinning Guide
300-360 Skinning Guide
Go to Thrallmar and find Moorutu if you are Horde player, he will teach you Master Skinning. For Alliance go to Honor Hold and find Jelena Nightsky. The paths on the map are pretty straightforward. Just follow those paths and when you reach 330, go to Nagrand.
360-450 Skinning Guide
Learn Skinning Grand Master.
Kill Gorillas, this place is also one of the best place to farm Borean Leather.
Learn Skinning Illustrious Grand Master.
At the Pale Roost, stone giants are throwing rocks and knocking down Stone Drakes. When the drakes land, they will have about 50k HP left. They drop only Savage Leather or Blackened Dragonscale, no leather scraps. The drakes have a really fast respawn rate, and for elites, they are very easy to kill.
Learn Zen Skinning.
Valley of the Four Winds
Kill Wyrmhorn Turtles near the small lake.
You can find more farming places if you visit my Exotic Leather farming guide.
Kill scorpions at Dread Wastes.