Leveling your Skinning will be easy, but you will have to run around and skin hundreds of mobs. Skinning is the best combined with Leatherworking.
I recommend using Zygor's 1-60 Leveling Guide if you are still leveling your character or you just started a new alt. The guide is in a small window on your main screen in-game. All the detail that you need to complete the quests are included. You’ll never have to switch back to a website, or even the in-game main map to see where you have to go or what’s next. And if you are low on gold, I recommend trying this Gold Making Guide, it can help you to make a lot of gold.
Learning Legion Skinning
You can learn Legion Skinning by simply skinning mobs at the Broken Isle until you get Stonehide Leather Sample or Stormscale Sample. It's not 100% drop rate, but you should get it after a couple of mobs.
The reward for these quests is [Legion Skinner]. You only need to get one of these quests, you don't need both.
Don't forget to enchant your gloves with [Enchant Gloves - Legion Skinning]! This enchant brings skinning time down from 1.5 seconds to 0.5 seconds.
Leveling 1 - 100
Keep in mind! In Legion, several people can tag the same mob and still get loot. So, if someone tagged your mob but he didn't loot the corpse, you can't skin the mob.
Please note that even if a mob is red/orange to you, this doesn't guarantee that you'll get a skill up. It's more likely, but not to be expected every time.
These are level 45 mobs, so lower levels can't farm here.
There are a couple of elite mobs patrolling around this area, you should avoid them, I think it's not worth to kill them.
When the Bloodgazer Swarm! world quest is active, there will be a lot of players there killing these mobs. So you will see dead animals everywhere, but most people don't loot the mobs, so sometimes it's actually worse to level here when the world quest is active.
You can find a lot of Saberfang Worg at the marked area.
This one is also the great place to farm Big Gamy Ribs. Sated Hillstrider will constantly keep spawning around the marked area.
I hope you liked this Legion Skinning leveling guide, congratulations to 100!