Entry is secured by looting a Key to the Palace of Lei Shen from any creature on the island, then heading over to find Taoshi with the Shado-Pan in their cave, where the Throne of Thunder raid entrance is. The key is used to start the scenario, via a quest.
Bashiok has confirmed that players can, unfortunately, only obtain a drop of this key once per week. Once you have looted a key, you will not find another on that character until the week is up, no matter how much you farm for them. This is likely a measure to keep the number of runs through the Treasure Room in check, as runs on the PTR could easily net several hundred gold, not to mention a plentiful stash of Motes of Harmony, Elder Charms and the like. Having a source for these sorts of things that was only limited by the number of mobs a player is willing to kill could have resulted in some minor issues. Bashiok does add that "Additional keys can potentially drop from other select sources, but are extremely rare and not something you can try to farm."
What's more, the same is true for Shan'ze Ritual Stones, used to summon elites. Only one stone can be looted per character per week. Hit the break for Bashiok's full post.