Go to the lady with the pikachu in Verdanturf town and talk to her.
If she says "Your pokemon couldn't possibly love you anymore. I even feel happy seeing it."
Then it's max.
Go to Verdanturf, then go into the bottom left house and talk to the lady.
You have to have the Pokemon whose Happiness you want checked in the first slot in your party.
If the Happiness is maxed, she'll say something like "It couldn't possibly love you any more. I even feel happy seeing it."
to 'train' happyness is easy, get acro and go to a mud spotand let it go up by putting something heavy on the up-button, it'll rais it's points with 1 per 512 steps or something
Go to Verdanturf and go into the house right below the Battle Tent/Contest Hall. She has a Pikachu next to her. If you talk to her and she says "It can't possibaly love you any more," then you have maxed out happiness of the first Pokemon in your party.