Right in the beginning of the game, you can go up to different people and press "A" to interact with them. You'll be given a choice either to shake hands ("A") or belch ("Y"). Doing either to register one expression. Do so for 20 different people to unlock this.
Note that interacting with your dog by whistling ("A") and then doing either pet ("A") or tell off ("X") will count as one expression as well.