Last night, my hunter dropped enchanting and switched to skinning in order to help level his leatherworking through Wrath of the Lich King. I figured I'd just do some of the skinning required and then get back to it later in the week, but it was so fast that I finished it all in two hours. Here's how I did it. (note: I'm Horde, but at the end I give some notes for Alliance players to use this guide also)
First of all, this is a guide for a level 70+. While you could start this at nearly any level, some of it really does require that you be at least 65, and better to be 70 since there are level 60 dungeons involved that you'll need to solo.
Also, I'm horde, so your mileage may vary if you're alliance, though you could go to all of these areas (it's just less convenient). To prepare, you really do want to be bount in Shattrath or Dalaran (unless you're a mage and can easily flit around from city to city).
Near Undercity and SFK
OK, so to start, get the training for apprentice skinning and get yourself to Brill, outside of Undercity. Kill the dogs and bats around that area until you get to 50. The trainer is between Brill and Undercity, on the road that leads to the Bulwark. Go train at 50 and go back to the dogs until you start skipping skillups (this is the pattern throughout: you go to an area until you need to train or you start getting less frequent skillups). At around 90-100 skill, you'll want to move on to Silverpine Forest to the southwest. Go all the way past the Sepulcher to the werewolves and wolves between the Greymane Wall and Pyrewood Village. These can all be skinned, and if it's night Pyrewood village is full of mobs that can be skinned (during the day, they're human). Once you get to 105, dash up to Shadowfang Keep and slaughter everything until you get to 150.
RFK and Feralas
Welcome to your next training level. Go train in Orgrimmar and then fly to Camp Taurajo and run south to the entrace of Razorfen Kraul. Enter the dungeon and take your first right and then a left off the ledge. You should be able to pass most or all of the Quillboar, but kill them if you have to, then get down into the area with the boars. Kill all of the boars and skin them. it's a long path that turns left at the end. Once you've wiped them out, leave the instance and reset it (right click on your unit frame and select "Reset all instances") and then do it one more time. You should be at or near 225 by now, so leave the instance and head to Feralas on foot (through Thousand Needles). Don't bother flying.
Go to Camp Mojache if you need to sell/mail items off. If you have not yet hit 225 skinning, then you can kill a few wolves and bears near the Thousand Needles border. These should be at the limit of your skinning ability. Once you hit 224, train in Mojache and continue to skin the bears and wolves near the camp until you start to green out. At that point, go sell to free up inventory and then on to the Dire Maul area to the west and then travel south to find the Hippogryphs. Skin these until you start to green out and then head into Dire Maul to the north.
Outside of Dire Maul, kill and skin the patrols of dogs until you hit 290 (you should already be quite close to this) and then go into the northern most entrance from the large courtyard. This takes you directly into Dire Maul North. If you take the western of the two doors along the north wall you will come in directly above a pit area with a boss and several packs of non-elite dogs. You will have to kill the packs of dogs in groups since they all come when one is pulled. If you're not an AoE class, this might take some time, but you'll get through it. Kill them and skin them until you hit 300.
Outland: All Hellfire, All the Time
Now that you've hit 300, go to Outland and train in Thrallmar, sell whatever you need to and leave Thrallmar and go east to the hellboars outside. The red-skinned hellboars are skinnable at your level. Skin them until you start to green out (which happens quite fast) and then go to Razorthorn Trail which is at the very southern edge of the rampart wall that divides the zone down the middle. There are ravagers in this area which you can kill and skin until you hit 350. You just want to march up and down the path. I ended up killing ravagers on one side going up and on the other side going back down, which worked out well, since anyone who was leveling in the area could keep to the other side and not be bothered by me.
Grand Master training
Now you're able to train Grand Master Skinning in Dalaran or Vengence Landing to begin in Northrend. Welcome to the two-hour 350 mark! From here, if you're level 70 you can just skin as you level. If you're 80 already, then you'll have to wait for my Wrath skinning guide...
For the Alliance
Alliance characters can probably substitute Loch Modan for Silverpine Forest and then go to SFK after. Everything else pretty much maps to the Alliance except for where they train in Feralas.