Begin by setting up your environment. Install Python and necessary libraries such as `requests` for API calls and `elasticsearch` for interacting with Elasticsearch. Ensure Python is correctly installed and configured on your system.

Obtain an API key from Polygon.io by signing up for an account. With this key, you can authenticate and make requests to the Polygon Stock API. Use `requests` in Python to fetch stock data. For example, use `requests.get` with the appropriate endpoint and query parameters to retrieve data.

Once you receive the data from the API, you'll need to parse the JSON response. Use Python's built-in `json` module to convert the JSON string into a Python dictionary. This will allow you to manipulate and extract the necessary data fields for insertion into Elasticsearch.

Before inserting data, create an index in Elasticsearch where your stock data will be stored. Use Elasticsearch's HTTP API to create an index with a suitable mapping. Define the fields and data types that match the structure of the data you plan to insert. You can use `curl` or Python's `elasticsearch` client to achieve this.

Transform the parsed data into a format compatible with Elasticsearch. This often involves converting timestamps to the appropriate format and ensuring that numeric and text data types align with your index mapping. Create a function in Python that formats each record accordingly.

Use the `elasticsearch` Python client to insert data. Connect to your Elasticsearch instance, and use the `index()` method to add documents to your index. Iterate over your transformed data and insert each record. Handle exceptions to ensure robustness, such as reconnecting on failures.

After data insertion, verify that the data is correctly stored in Elasticsearch. Use Elasticsearch's search API to query your index and check that the documents are present and correctly formatted. This can be done using Python to programmatically check, or manually using tools like Kibana for visualization.

By following these steps, you can efficiently transfer data from the Polygon Stock API to Elasticsearch, ensuring that each component is properly configured and data integrity is maintained throughout the process.