How to increase your Buddy's happiness with you in Pokémon in Pokémon Go Buddy.
Play with them.
Feed them berries.
Take your snapshot.
Battle with them.
Walk with them.
Visit a new place with them.
These activities can only be done daily but not continuously. Doing it daily will allow your level of happiness to increase enough to become a Great Friend and help you capture other Pokémon.
Now that you know how to get your friend to help you catch other Pokémon in Pokémon Go Buddy, your Buddy can help you get new Pokémon to increase your list and move faster and faster.