In Pokemon XY, I want one of my Pokemon to have its hidden ability. If I put it up on the GTS, and have my friend trade me for it, then trade it back to me, will it gain its hidden ability?
Bulbapedia says: "Where possible, all Pokémon obtained from the Pokémon Global Link, either via the Pokémon Dream World or a Global Link promotion, will always have their Hidden Ability."
Does this apply to gen VI?
"Global Link" is just Nintendo's term that encompasses all their online services (including the Global Link Website), which includes but isn't limited to Wonder Trade, GTS and the Pokémon Dream World. In other words, every time you read "Global Link", they simply mean 'online'.
The Bulbapedia quote says it all:
"Where possible, all Pokémon obtained
from the Pokémon Global Linkonline, either via the Pokémon Dream World or a Global Link promotion, will always have their Hidden Ability."
So unfortunately no, trading with your friend over GTS isn't going to get you the hidden ability.
However, if someone puts up a Pokemon on the GTS already with the Hidden Ability, and you trade them for it, then you will get the Hidden Ability. This is most likely how your friend got his/her Greninja with its Hidden Ability (unless someone was very kind and put it through Wonder Trade).
Abilities in general (not just Hidden ones) are generated when the Pokemon is first encountered. this means either
In other words, there is no way to change a Pokemon's ability via trading. (Caveat, unless there's a Pokemon that evolves when trading, and it's evolved form has different Abilities, although I cannot think of any)
So I can catch wild Pokemon with Hidden Abilities?
Only in Horde battles, and even then only rarely. Plus the types of Pokemon that appear in horde battles are few in number, and doesn't include Froakie or any other starter line at all.
So why does everyone have Hidden Abilities online?
Everyone wants Hidden Abilities as they are generally better than the Stock abilities (although this isn't always the case). Either way, there's the stigma attached to them: Because they are 'rarer', they must be 'better'. Everyone is therefore striving to get them, and that's why you see so many of them.
So where can I get Pokemon with Hidden Abilities?
As Unionhawk states, Friend Safari is your best bet. You'll need a friend of the right type (Water for Frogadier), and then Frogadier can appear in Slot 3, possibly with it's hidden ability.
Side note: One way I've found extremely helpful to check a Pokemon's ability in battle is by using the move Worry Seed, which Budew learns. Worry Seed will change the targets Ability (in battle only) to Insomnia, but before it does, it will flash up the Pokemon's Ability.
