Each of the three birds will be in an egg.

The first Mythical bird is Moltres (he is in the Volcano level), he will be easy to find since his egg is blocking your path. all you have to do is hit the egg with pokemon food or pester balls and a moltres will emerge from the hot lava

To get Zapdos you must lure pikachu to the egg sitting in the tunnel then play a pokeflute. If you did it right pikachu will hit the egg and he will shoot the egg out and the egg will blow up revealing Zapdos.

Articuno: Play your Pokeflute when you see the Jynx and the egg.