To get the Shiny Charm, you'd need to follow the following stamps.
First, you will need to catch every pokemon in the national Pokedex!
These do not include #151 MEW, #385 Jirachi, #251 celebi, #385 Deoxys, #491 Darkrai, #492 Shaymin, #493 Arceus (You are not required to catch these for the shiny charm).
Now you need to go to the lakefront on route 213.
Click the Town Map option.
Enter this house.
Now talk to the Game Director to get the shiny charm!
You obtained a shiny charm!
Put the shiny charm in your bag's key items pocket.