Begin by setting up your development environment. Ensure you have Python installed on your machine as it's a versatile language for handling HTTP requests and database operations. Additionally, install MySQL and set up a database where the data will be inserted. You'll also need to install required Python libraries such as `requests` for API calls and `mysql-connector-python` for interacting with MySQL.

Register for an account at Polygon.io and obtain your API key. This key is essential for authenticating your requests to the Polygon Stock API. Make sure to read through the API documentation to understand the endpoints related to the stock data you wish to retrieve.

Using Python, write a script to make HTTP GET requests to the Polygon Stock API. Use the `requests` library to send the request, appending your API key for authentication. For example, to get stock prices, you might request data from an endpoint like `/v1/last/stocks/{ticker}`. Parse the JSON response to extract the needed data fields.

Once you have the data, transform it as necessary to fit into your MySQL database schema. This might involve selecting specific fields, renaming keys, or converting data types. Ensure that your data is clean and matches the structure of your MySQL table to avoid errors during the insertion process.

Use the `mysql-connector-python` library to establish a connection to your MySQL database. Create a connection object with the appropriate credentials such as host, user, password, and database name. Verify that the connection is successful before proceeding to data insertion.

With an active database connection, use SQL `INSERT` statements to add the data to your MySQL tables. You can use a cursor object to execute these statements. Depending on the volume of data, consider using batch inserts for efficiency. Ensure that you handle exceptions to catch any errors during the data insertion process.

After successfully inserting the data, close the database connection to free up resources. Implement error handling throughout your script to manage potential issues such as network failures, API rate limits, or database errors. Logging errors and successful operations can help with debugging and maintaining your data pipeline.

By following these steps, you can effectively move data from the Polygon Stock API to a MySQL destination without relying on third-party connectors or integrations.