First, obtain API access by logging into your Drift account and navigating to the developer settings. Create a new application to receive an API key or token. This token will authenticate your requests to Drift's API endpoints.

Determine the specific data you wish to migrate, such as conversations, contacts, or events. Refer to the Drift API documentation to understand the structure and available endpoints for the data you need.

Develop a script using a programming language like Python or Node.js to make HTTP GET requests to the Drift API. Use the obtained API token for authentication. Ensure that the script can handle pagination if the data volume is large, as APIs often limit the amount of data returned in a single request.

Once the data is fetched, parse the JSON response and transform it into a format suitable for MySQL. This involves mapping JSON fields to the corresponding columns in your MySQL database tables. Plan the schema of your MySQL tables to match the structure of the API data.

Use a MySQL client library suitable for your programming language to establish a connection to your MySQL database. Ensure that you have the correct credentials (host, username, password, database name) and the necessary permissions to insert data.

Write a function in your script to insert the transformed data into the MySQL tables. Use SQL `INSERT` statements for this purpose. If you're inserting large datasets, consider using batch inserts to improve performance. Additionally, handle potential conflicts or duplicates by using `INSERT IGNORE` or `ON DUPLICATE KEY UPDATE` clauses as needed.

After completing the data insertion, validate the process by querying the MySQL database and checking if the data matches the source data from Drift. Implement logging within your script to capture any errors or issues during the data transfer. Set up a monitoring process to ensure ongoing accuracy if this is a regular data migration task.