Background: Effective hospital discharge planning is crucial, particularly in educating caregivers on handling medical devices. This education helps manage the patient’s signs and symptoms, prevents post-discharge complications, and reduces early readmissions. This study aimed to understand aspects involved in the acquisition of mastery by home caregivers, in handling care of a patient who just underwent gastrostomy, after educational intervention during hospitalization and telemonitoring upon return home. Methods: Qualitative descriptive study. It followed 15 caregivers of people with percutaneous endoscopic gastrostomy. The intervention took place between November 2022 and July 2023 in the neuromusculoskeletal unit of a Brazilian university hospital. Results: The educational intervention had four stages. In stage 1, caregivers felt confused and uncertain about managing PEG. By stage 2, they expressed a desire to be capable of handling care, especially in the event of potential complications, and showed increased awareness and engagement. Stage 3 highlighted the effectiveness of hands-on training with feedback from professionals. In stage 4, during monitoring, several complications were noted, including granuloma formation in the stoma, tube obstruction, and accidental tube loss. However, caregivers demonstrated the ability to handle these situations, indicating the effectiveness of the training and telemonitoring interventions. Conclusions: Nursing professionals should consider various factors when training caregivers in a hospital setting, including providing adequate space, allocating sufficient time for educational interventions, offering both theoretical and practical demonstrations, ensuring effective communication, and taking into account the caregivers’ context, as they play a direct role in acquiring a safe and effective skill set.