Ok, I think this is the same. If anything I say is incorrect please let me know and I'll change is ASAP.
EDIT: I just looked over the competition page you are looking at and that competition isn't open yet. You can't sign up for it until February 5th through 12th.
1st: Make a Pokémon Global Link Account. Here is a link in case you can't find it.
2nd: Register your game. After you create an account, there is a spot to register your game. This will require your 3ds/2ds and game.
3rd: Go to the tournament page in your account and sign up.
A few things to note are:
The tournaments usually have a max. If this is reached you can't join.
They give you a week sign up period, you cannot battle during that time. You also can't sign up after that ends.
I'm pretty sure this covers it all. The rules are in the link you posted and are pretty self explanatory. If you have any questions please ask!
Hope this Helps!