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According to sources on the Blizzard forum, the secret level is called Whimsyshire:

Whimsyshire is essentially a single-level dungeon, much like the dungeons you find randomly while exploring the wilderness. Just like these random dungeons, it has chests and other lootable objects, plus a plethora of monsters, including some champion and unique monsters.

Level-wise, it contains monsters and loot that are roughly on par with the first act of Nightmare (if you're visiting the Normal variant - I assume that it is roughly on par with the first act of the difficulty one harder than the difficulty you enter the portal in) - nothing super difficult or super awesome. It may be worth visiting/farming if you've cleared the difficulty you're on, but are having trouble with the first act of the next difficulty. Otherwise, it's probably likely to be underwhelming.

In order to visit Whimsyshire, you must craft a Staff of Herding, and take it to a specific area in Act 1.

The Staff of Herding

Unlocking Whimsyshire requires a Staff of Herding, which can be crafted at the blacksmith for 50,000 gold and requires the following items:

Black Mushroom - Cathedral Level 1

The mushroom in a patch of mushrooms that occasionally spawn on level 1 of the Cathedral (screenshot). When you enter the room, your hero will remark about the unusual mushrooms. The room it spawns in always looks the same so you can look for it in the minimap. (minimap screenshot).

If you're past this point in the story, go to Act 1, Mission 4: Reign of the Black King. Travel from the New Tristram waypoint to the Cathedral Garden, and then walk out the gate and back around to the front of the Cathedral. Open the door and descend to Cathedral Level 1.

Leoric's Shinbone - Leoric's Manor

The shinbone is found occasionally in the fireplace of Leoric's Manor. From the entrance to the manor, walk forward to the staircase, and hang a right. The room with the fireplace is on the first floor on the right side. A large painting of an old man hangs over the fireplace. If the shinbone is present, there will be logs in the fireplace. Click the logs to get the bone. (screenshot).

If you're past this point in the story, return to Act 1, Mission 9: The Imprisoned Angel. Take the waypoint to Leoric's Manor. Backtrack through the manor into the room with the large statue overlooking a double staircase, and then head into the room to the northeast on your minimap.

Wirt's Bell - Caldeum Bazaar

Squirt the Peddler sells this item at the Hidden Camp in Act 2. This vendor was moved in patch 1.0.4 to stand just up and to the right of the waypoint in the Hidden Camp. The item is on the "Miscellaneous" tab. The cost for the bell is 100,000 gold.

Liquid Rainbow - Mysterious Cave in Dahlgur Oasis

From the Act 2 waypoint "Path to the Oasis," travel southeast. Zaven the Alchemist may be here, and if so you can save him to access the cave. (screenshot) The item is in a the "Mysterious Chest" which also may not spawn, even if you're in the right dungeon.

If you're past this point, load Act 2, Mission 7: Blood and Sand. Take the "Path to Oasis" waypoint, as noted above.

Gibbering Gemstone - Caverns of Frost in Fields of Slaughter

This item drops from a "purple" class monster named Chiltara that has a chance of spawning in the second level of Caverns of Frost, a random dungeon that may or may not appear in the Fields of Slaughter. Other dungeons may appear here, but you can only find this item in the Caverns of Frost.

From the waypoint "The Bridge of Korsikk" travel almost due east. You should see a small cluster of debris that has a small, U-shaped indentation in it. (screenshot) The dungeon may spawn northwest, or southeast of this debris. (There are other potential locations, but these are the fastest 2 to check) Ensure this is the Caverns of Frost before clearing it!

If you've passed this point, load Act 3, Mission 6: Siegebreaker. Take the waypoint to "The Bridge of Korsikk" as noted above.

Plans for the Staff of Herding - Great Span

This item is a random drop from Izual, who is a midboss on the Great Spire. Unfortunately, there's not a "fast" quest checkpoint for this one - you're going to have to start Act 4, Mission 4: Prime Evil, and then fight through the Silver Spire Level 1 in order to get to the Great Span.

Izual tends to favor attacks that freeze you in place, so bring any skills you know which can break his freezing spell. Many of the "movement" skills (ie, Spirit Walk) can do this. If you kill Izual and he does not drop the plans, you'll have to exit out, reset the quest to "Quest Start" and start over again, fighting through Silver Spire Level 1.

For this reason, I'd suggest being overleveled before you attempt this - fighting this area repeatedly is likely to be time consuming and frustrating if you can't just obliterate everything quickly.

A few additional notes:

• Given that most of these are random drops, in some cases from random monsters in random dungeons you can expect to invest a decent amount of work in getting each of these components. You may try to get the Shinbone a dozen or more times, for instance.
• If you search the indicated area and don't find the item/dungeon/boss, you'll have to exit back out to the character selection screen and resume the game again to get another chance.
• These items may spawn in other locations; I've listed the locations where I or others have had good luck finding them.  
• The items are marked as "account bound" - so you won't be able to buy these at the auction house, for example.

The Staff of Herding you create from this recipe only unlocks the Normal difficulty variant of Whimsyshire. To unlock Whimsyshire on higher difficulties, you'll need to upgrade the staff. You can find more information about how to find the plans for these upgrades in this question:

How do I get higher difficulty Plan: Staff of Herding?

Opening Whimsyshire

Once you have the staff, travel to New Tristram by choosing any of the quests in Act 1 past the point where the road to Old Tristram is open. From the New Tristram waypoint, follow the road towards Old Tristram. When the path turns to the right past the abandoned houses, you will find a fissure in the ground along the southern edge of the path. Nearby will be the Ghost of the Cow King. (screenshot) With the Staff of Herding in your inventory, clicking on the Ghost will trigger a few lines of dialog, and then the fissure will open.

Other related questions:

Can I enter Whimsyshire if I follow someone in my party with the Staff of Herding?
Is there any achievement related to Whimsyshire?
Sharing Whimsyshire crafting materials between difficulties
Do the Staff of Herding crafting items drop in all difficulties?
Will a higher level Staff of Herding open the lower difficulty Whimsyshire?
Can you access the secret level in Diablo 3 more than once per difficulty?

At the moment your best bet is to follow Blizzard's Twitter updates at https://twitter.com/#!/BlizzardCS. They've kept regular updates on Diablo III server availability, including the current maintenance.