[Guide] Getting Your White Core Hound

White Core Hound? Want it? YES YOU DO!

BigRedKitty calls it the "Puppy Dog of Doom". I call it the only Core Hound that actually looks like a beast (the others look like some sort of demon, and we're definitely not warlocks).

Ok, so a couple of questions have been asked as to how you get it. So here's a guide.

Briefing:
Your target: The Kurken, a level 12 Core Hound on Azuremyst Isle. Wowhead. Petopia. NOTE: It's an EXOTIC pet, so you'll need the 51 pt BM talent (Beast Mastery)to tame it.
Here's a map:

Azuremyst Isle: Now Even More Exotic!

Details: the target lives in a cave (Stillpine Hold) with some deranged Owlkin. It's the object of a quest, so be nice to any level 10-12 draenei running around.Now if you're Alliance, that's all you need to know. Go get it, or go find a real challenge.

If you're Horde things get a bit more tricky.
Firstly, Azuremyst Isle is hostile territory. And there's no direct transport.

On the plus side, you need to be at least 60 to tame the thing in the first place, so at least you won't have a hard time getting there, it will just take a while.

Before you go: STABLE YOUR CURRENT PET, or prepare to abandon it.

How to get there (Horde):
The route is Ashenvale -> Darkshore -> Azuremyst Isle.
More specifically, you need to get to Darkshore, and then head to the Auberdine Docks (it's an Alliance town, and not a problem for a 60+).

Darkshore: Alliance territory

The best way to get to Darkshore is to fly to Zoram'Gar in Ashenvale (from Orgrimar), head a bit east to the road and take it north (the road on the western side of Ashenvale, not the one to Felwood), Splintertree Post also works.

Ashenvale, Horde Flight Paths shown with a *

If you don't have the Zoram'Gar FP or Splintertree Post, head north from the Barrens through the Mor'Shan Rampart and into Ashenvale. And pick up the FP while you're at it. If you don't know where the Barrens are, look up Chuck Norris, or go roll Alliance (although if you don't know where the Barrens are, you won't get the Chuck Norris reference either).

For the Horde: Showing Route from Orgrimar

Ok, you've made it to Auberdine. You're at the docks (which can be found if you ride through the inn). You can't read the signpost that points to Azuremyst Isle (because Orcs can't read), so let's make sure you get on the right boat: the left pier goes to Stormwind, which is some Alliance village or something; the right one goes to Teldrassil, some other Alliance hovel; the middle one goes to Azuremyst Isle, which is still infested with Alliance, but also has one of the coolest pets in the game on it.

Directions: The Blue Thingie is You, the Black Cross is the Docks. Paint Rocks.

Take the boat. Wait for it to cross the water. Get off the boat. Check out that Wowhead map linked above. You're at the docks south of the Exodar. Head north along the road (western side of the isle), but go around the Exodar (hint: the guards are now level 75, I found this out the hard way when I thought I could take a shortcut through).
Keep an eye out for a bunch of hills on your right, if you've reached the bridge to Bloodmyst Isle, it's a bridge too far. Stillpine Hold shouldn't be too hard to find if you keep an eye on your map. The cave entrance is from the south.
Don't kill any Draenei if you're on a PVP server, let them grow into worthy foes. Feel free to kill any gnomes you see.
Enter the cave (Stillpine Hold). Your target is at the back of the cave, by a lake. As you go in, there's a little path on the left that dips down and takes you straight there, but if you miss it you'll get there eventually. Tame it. Hearth out and stomp around Shattrath, or go raid the Exodar.

Now if you want to be manly (or womanly) and you need a MC one, check out It's Gotta Be Orange! on BRK.net. It's an excellent guide.

Personally I really like my white Core Hound. It looks awesome.

Now /shoo and get taming!

EDIT: now with pictures for the illiterate.