From what I've found in my internet research, these are the steps you have to follow to get Garchomp:
1 - Make sure you actually participated in the Sinnoh Classic.
2 - Go to http://3ds.pokemon-gl.com/
3 - Log in (you should have had to log in to register for the competition anyways)
4 - There should be a little notification or something.
5 - Click on that and it should give you your Garchomp code
6 - Enter the code in the "Receive Mystery Gift" screen
7 - Obtain butt-kicking dragon shark.