How to wake up the Snorlax that’s in Pokemon village

There are 3 Kalos (Generation VI) legendary Pokémon, and 4 Kanto (Generation I) legendary Pokémon available in Pokemon X & Y.

Kalos Legendaries

• #716 Xerneas / #717 Yveltal
  • Found as part of the story (Team Flare's HQ) at level 50.
  • Version Specific (X has Xerneas, Y has Yvetal)
  • Both are stationary
• #718 Zygarde
  • Available after the Elite 4, in both X & Y
  • Found on the bottom floor of Terminus Cave at level 70
  • stationary
• #719 Diancie
  • Available only through a special event
• #720 Hoopa
  • Available only through a special event

Kanto Legendaries

• #144 Articuno / #145 Zapdos / #146 Moltres
  • Randomly encountered wandering after defeating the Elite 4.
  • You can only encounter one, which is dependent on which starter Pokemon you chose:
    1. Chespin -> Articuno
    2. Fennekin -> Zapdos
    3. Froakie -> Moltres
  • They will flee automatically 12 times when you encounter them, after which they will go to the Sea Spirit's Den where you can finally battle them. Source.
• #150 Mewtwo
  • Available after the Elite 4, in the cave in Pokemon Village:

    After defeating the Elite Four, a man will stop blocking a cave within the Pokémon Village. In this cave, you will find nothing but a solitary Mewtwo with its back against the door. Interact with it and a cutscene will occur where it notices you and attacks. After defeating it, you will receive the Mewtwonite X or Y item depending on your version. - Source

I had the same trouble finding this option at first, and argued with someone at length that this just wasn't possible. The letters list does seem to be like the old GTS; you can only search for Pokémon you've at least seen.

But if you scroll all the way down past "Z" You'll notice a button called "What Pokemon?" Click on this and it will bring up a text input, where you can manually type in the name of a as-yet-unseen Pokémon and search for it.

It is not possible to shorten a Pokémon's name to search for it. Searching for "Geodude" will return results, but not "Geo". However, do be aware that it does not inform you whether or not the name you typed exists - only that there were (no) results after you search. Also as there are a number of Pokémon that do not normally occur in the Kalos region, searching for them will likely not produce any result until Nintendo releases the Pokémon Bank and this generation's transfer tool.

Also, as event-only Pokémon cannot be traded on the GTS, there are none listed. So if you've manually searched for "Mew" or "Celebi" or any of the other event-distribution Pokémon, it will not yield any results, as there ARE none of those Pokémon for trade on the GTS.