Jonathan Simon provides a detailed walkthrough of migrating from a self-managed Elastic Stack to Elastic Cloud using a snapshot and restore method with Amazon S3. The process involves setting up a self-managed Elastic Stack using Docker, creating a search index, and then migrating the stack, including Observability and Security data, to Elastic Cloud. Simon emphasizes the importance of updating data collectors to point to the new Elastic Cloud deployment after migration. The guide suggests that while managing one's Elastic Stack can be beneficial initially, Elastic Cloud offers enhanced functionality and ease of management, encouraging users to take advantage of a free 14-day trial to explore its benefits.