In response to Heroku's discontinuation of its free plans, developers are advised to consider migrating from Heroku Postgres to CockroachDB serverless, which offers a robust free tier and distinct advantages such as increased storage capacity and flexible scaling options. The process involves several key steps, including exporting the database schema and data from Heroku using pg_dump, creating a CockroachDB account, setting up a serverless cluster, and utilizing CockroachDB's schema conversion tool to facilitate the migration. The tutorial provides detailed instructions on importing the data using various methods, including local file imports and cloud storage commands, ensuring that even those unfamiliar with the intricacies of database migration can follow along. The guide underscores the benefits of CockroachDB's cloud-native architecture, which allows for automatic scaling and customizable spending limits, making it an appealing alternative for developers seeking a cost-effective and scalable solution after Heroku's changes.