Building a pet care app like Chewy involves several steps. First, research the market to understand your niche and target audience. Then, define what makes your app unique. Next, design a user-friendly interface and choose the technology to build it. Develop core features like pet profiles, product search, and secure payment. Consider adding features like auto-refill subscriptions, vet consultations, and social aspects for a well-rounded experience. Finally, test the app thoroughly before launching it to the public.