Begin by visiting the Google PageSpeed Insights API documentation. You�ll need to understand how to make requests to the API to fetch performance data for a specific URL. Familiarize yourself with the request structure and required parameters, such as the URL and API key.

To interact with Google PageSpeed Insights API, you'll need an API key. Visit the Google Cloud Console, create a new project if necessary, and navigate to the API & Services section. Enable the PageSpeed Insights API and generate an API key. This key will authenticate your requests.

Use a tool like `curl` on the command line or a script in a programming language like Python to make an HTTP GET request to the PageSpeed Insights API endpoint. Incorporate the URL you wish to analyze and your API key into the request. For example, in Python, you could use the `requests` library to fetch the data.

Upon receiving a response from the API, it will be in JSON format. Parse this JSON response to extract the necessary performance data. If using Python, you can use the built-in `json` module to load the response data for further manipulation.

Identify and extract the specific metrics or information you need from the parsed JSON data. This could include performance scores, loading times, and other relevant insights. Ensure you structure this extracted data in a way that suits your needs for local storage.

Once you have the necessary data, format it into a JSON structure suitable for saving locally. This may involve creating a dictionary or list in Python and converting it back to a JSON string using `json.dumps()`.

Finally, write the formatted JSON data to a file on your local machine. Open a new file in write mode and use the `json.dump()` function to write the data. Choose a clear and descriptive file name and ensure the file is saved in a directory where you can easily access it later.
By following these steps, you'll be able to efficiently move data from Google PageSpeed Insights to a local JSON file without relying on third-party tools.