You need to complete each battle course (Double, Triple, Rotation) perfectly. By that I mean you need to defeat each opponent (waiter/ waitress etc.) in the number of turns they recommend. If you miss something/ aren't sure how many turns were correct, you can tell by the reward at the end. At Restaurant Le Wow, if you get it perfectly, you'll get 25 Balm Mushrooms. Any less and you either took too many or too few.
This Serebii article shows how many turns are required for each battle in each restaurant and what Pokemon are used:
Serebii - restaurants
From personal experience, it's actually quite annoying to get it right, because the waiter in Le Wow spams Protect, so you really need some luck to get it right. Taunt can help, but you do waste a turn using it, and it'll be pointless if he uses Protect.