Where do you get the first generation legendaries in X and Y?

Solution 1:

Okay so after gathering some more information, the three birds aren't like normal roaming legendaries (eg Latios/Latias in Gen 3).

Firstly, as @RavenDreamer mentioned, you must defeat the Elite Four. Then you can get MewTwo (which is a normal battle) in the Unknown Dungeon at the Pokemon Village.

Then, you must hunt down a legendary bird. It depends on your starter:

• If you chose Chespin, the legendary will be Articuno
• If you chose Fennekin, the legendary will be Zapdos
• If you chose Froakie, the legendary will be Moltres

The method of finding a roaming legendary is the same as other generations.

HOWEVER, after finding the legendary, it will immediately flee (you don't get even get a turn).

You must find the legendary 8-12 more times, after which it will reside in the Sea Spirit's Den, where you can legitimately (i.e it won't flee) fight.

Solution 2:

After you beat the elite four, you can access mewtwo at the bottom of the unknown cave in pokemon village.

Likewise after you beat the elite four, one of the three legendary birds (the one weak to your starter) will stay roaming the Kalos region. You will have to chase it down, like other wandering legendaries.

It is unknown cave in pokemom village for mewtwo.