To collect both standard RDS metrics and native MySQL metrics, users can access RDS metrics via Amazon CloudWatch and query server status variables, the performance schema, or use a monitoring tool with a CloudWatch integration. The process involves connecting to the database instance remotely using tools like SSH, querying server status variables, enabling the performance schema, or using a monitoring tool that integrates with MySQL. These methods provide insights into MySQL performance, allowing users to set up alerts and visualize metrics for a comprehensive view of their database instance's health.