I've never really gone shiny hunting, but I have heard of things.
First is the
"masuda method", which is hatching shiny pokemon from eggs (supposedly takes a lot of time and patience). I know it works in X/Y, though I don't know if it works in ORAS (it should, as ORAS is still Gen VI).
So, this method works for both games, but requires breeding (and patience).
There's also chain fishing, which is consecutive catches in the same spot while fishing (requires a pokemon with an ability such as "suction cups" to be in the front of the party).
In X/Y, Friend Safaris are probably the best way to get shinies. I found three shinies in friend safaris without even trying. I don't know if giving tips throughout the game increases the chance (I always tipped through the playthrough since I had plenty of money in X).
There's a method in X/Y using the Pokeradar, though it's extremely confusing and time consuming. If you can figure it out (instructions are
HERE), and want to give it a try, good luck. -_-
In ORAS, you can use the DexNav to shiny hunt. Someone wrote up a good explanation
HERE, and of course, I'm sure there are Youtube tutorials. One of my favorite Pokemontubers, aDrive, does shiny hunting via the dexnav method.