Quick Guide:
1-75 Durotar, Dun Morogh
75-155/165 The Barrens, Loch Modan, Wetlands
155/165-205 Thousand Needles, Arathi Highland
205-300 Un'Goro Crater, Feralas
300-360 Hellfire Peninsula, Nagrand
360-450 Borean Tundra, Sholazar Basin
Don't forget to buy the Skinning Knife
1-75 Durotar, Dun MoroghVisit any Skinning Trainer located in World of Warcraft, and learn Skinning Apprentice.
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.
From 1 to 75 you will start at Sen'Jin Village in Durotar and head toward Orgrimmar, while you skin every beast you see. When you reach Orgrimmar, visit your Skinning trainer and learn Journeyman Skinning. After that, fly to Crossroads which is located in The Barrens. Keep in mind, it's not guaranteed that you will reach 75, but if you won't reach it you can just still go to Orgrimmar, Skinning 50 will be enough too.
75-155/165 The Barrens, Loch Modan, Wetlands75-125 Skin the beasts you find while you head toward Camp Taurajo. Make sure that you have Skinning 125 when you reach the Camp, else Dranh at Camp Taurajo won't be able to teach Expert Skinning to you. From 125 to 165 head toward Thousand Needles and skin the beasts you see. To be honest, I feel sorry for Alliance players at this point of the Skinning guide. Horde players have such a good traveling roads, it's a lot easier to level Skinning as a Horde player than as an Alliance
155/165-205 Thousand Needles, Arathi HighlandFrom 165 to 205 just follow the path you see on the picture. Make sure that you have Skinning 205 before you leave Thousand Needles. After 205 go to Tanaris and fly to Feralas, at Feralas find Kulleg Stonehorn he will teach you Artisan Skinning.
205-300 Un'Goro Crater, FeralasFrom 205 to 230 just skin mobs around Camp Mojache, this one is doable for both Horde and Alliance. When you reach 230, mount up and head towards the Yeti cave, it's where you can see the 230-260 part on the map. If the Yeti cave is farmed by someone you can head to South and kill Hippogryphs. After you reached 260, follow the path to the 260-280 part. There is another Yeti cave there, but those Yetis are higher levels. When you killed all of them, you can find a lot of beasts in front of the cave. At Skinning 280 you can fly to Un'goro Crater, however you can stay here too, and skill up your skinning by killing the beast in front of the cave.
Feralas
Ungoro
300-360 Hellfire Peninsula, NagrandGo to Thrallmar and find Moorutu if you are Horde player, he will teach you Master Skinning.
Hellfire
Kill Talbuks and Clefthoofs. You can stop at 350 and go to Northreand, if you want to.
Nagrand
360-450 Borean Tundra, Sholazar Basin Hellfire Peninsula, NagrandGo to Northrend and learn Skinning Grand Master.
Borean Tundra
Kill Rhinos
Sholazar Bassin
Kill Gorillas, this place is also one of the best place to farm Borean Leather.