The common steps to scale a database as described by Tajus include: 1. Distributing the API to avoid a single point of failure, 2. Scaling the database vertically by adding memory and disk space, 3. Scaling the database horizontally by adding primary instances and replicas, 4. Using an in-memory database to speed up data reading, 5. Adding a search engine to handle large data volumes and replicating data in real-time using tools like Kafka.