Defeat the Elite 4. Depending on your starting Pokemon, you can encounter the corresponding Legendary Bird wandering around Kalos.
If you started with Froakie, Moltres will be available.
If you started with Chespin, Articuno will be available.
If you started with Fennekin, Zapdos will be available.
After encountering the bird, look it up in the Coastal Kalos Pokedex to find its current location. Walk there to challenge the bird again. Repeat the process and it will eventually go to Sea Spirit's Den, where you will have the chance to catch it.