YugabyteDB Anywhere provides an API to capture table-level size metrics, which can be used to track the growth of tables and databases over time. To do this, users need to create required database objects such as a database, sequence, and table to store the data. They also need to configure Python modules and environment variables with the necessary credentials and IP addresses. Once these are set up, users can capture metrics by connecting to the YugabyteDB platform API and storing the data in a persistent table using PostgreSQL. The data is then validated to ensure it has been successfully captured, and the process can be scheduled to run daily.