The cafe is a place where Pokemon can gather and relax, but you cannot interact with it beyond ordering drinks and food for yourself. There is no gameplay element where you can serve customers or manage the cafe.
However, there are other ways to interact with the cafe and its owner, Chatot:
* Ordering drinks and food: You can buy drinks and food from the cafe to regain HP and PP.
* Talking to Chatot: He might offer advice or information on your quests.
* Playing the "guess the song" minigame: Chatot can play a song and you have to guess the title for a reward.
If you're looking for a game where you can run a cafe, there are other options available, such as "Animal Cafe" for the Nintendo DS or "Coffee Stain Studio's" "Coffee Talk" for PC.