Instructions
Travel to Narcene, marked on your in-game map. If you have not yet been here, keep playing; the game naturally takes you here as you complete it.
Enter the PokeCenter in the middle of the city.
Walk to the right side of the building, where you will see a woman standing beside a Pokemon.
Press "X" to open your menu. Select "Pkmn," followed by the Pokemon whose happiness you want to check. Select "Move" and move it to the top of your lineup. The woman will only check the happiness of your first Pokemon, so you must perform this step for each Pokemon you want to check.
Press "A" while standing next to the woman to evaluate your Pokemon.