Neon's Free Plan provides developers with a robust platform to start building applications using Postgres, allowing for up to 20 projects, each with its own resource limits, such as 0.5 GB of database storage and 100 CU-hours of compute time per month. To maximize the utilization of these resources, users are advised to monitor each project separately, optimize compute usage by scaling down CPU allocations, and practice storage housekeeping by managing data growth through retention policies and cleaning up unused indexes and dead tuples. Additionally, developers should be mindful of network transfer limits by optimizing queries to avoid unnecessary data retrieval and manage ORM defaults. By adopting these practices, developers can effectively extend their use of the Free Plan, making it a versatile tool for prototyping, testing, or launching Postgres-powered applications.