I am aware that there are three 6th generation pokemon, but apparently you are able to get the legendary bird trio (Articuno, Zapdos, Moltres) and Mewtwo (for mega evolutions).
How do you get these pokemon in Pokemon X/Y?
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 first. Then you can get mewtwo (which is a normal battle) in the Unknown Dungeon.
Then, you must hunt down a legendary bird. It depends on your starter:
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.
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.
You have to encounter it multiple times, and then, it will move into sea spirit's den, which is off route 12, and you can battle the legendary bird of your choice.
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