First, the necessary information. Much like babies, happiny need plenty of sleep. Ensure they have a soft bed and warm blankets. Do not swaddle them but rather loosely cover them if they look cold. Feed them at least twice daily with either kibble or pureed fruits and vegetables, as well as milk for calcium. Baby formula, strangely enough, also works. Happiny will also need a litter box with standard poké filler, and this should be changed daily. Give your happiny a daily bath with gentle soaps in your sink or tub. Finally, happiny should be given durable, soft or plastic toys—never anything with small parts—as well as a polished, round stone that resembles a miniature chansey egg (an oval stone, in other words). Even if you don’t evolve your happiny, the stone does wonders for its mental health.
Now! As for integration, this is a bit tougher. If you still have one or both of her parents, allow them to help you with this. Let them show her that the rest of her team is friendly, and let them introduce her. If you don’t still have her parents or if you adopted her, start with the youngest, gentlest member of your team. Introduce that specific pokémon to her on its own as a playmate. Let that pokémon play with her and “babysit” her, as it were. Once she begins to trust that team member, introduce another one with the first one present. Work your way towards introducing her to your team one by one until she meets the fiercest, oldest members, and have each of your team members play with and care for her in turn. Introducing her to your team all at once may intimidate her, but going slow and allowing her to start with your most approachable members allows her to get comfortable with them at her own pace. Likewise, keeping the members she’s already befriended out as you introduce her to someone new allows her to seek comfort in the friends she’s already made.
Best of luck and congratulations on the new addition to your family, anonymous!
The Pokédex According to Bill 