1-60 Skinning Guide
Visit any Skinning Trainer, and learn Skinning Apprentice.Don't forget to buy a Skinning Knife! (I always forget it) After you bought the knife, just follow the zones listed in the guide. This knife does NOT have to be equipped.
Please visit my Leather farming guide if you want to farm leathers for Leatherworking!
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.
Horde:
Alliance:
60-110 Skinning Guide
Horde:
Alliance:
110-185 Skinning Guide
Horde:
Alliance:
185-205 Skinning Guide
Horde:
Alliance:
205-265 Skinning Guide
265-300 Skinning Guide
300-375 Skinning Guide
From here you will gain skills much less frequently, as you will see on the picture below.
360-450 Skinning Guide
Go to Northrend and learn Skinning Grand Master.
Kill Rhinos.