Begin by familiarizing yourself with the Statuspage API. Visit the official documentation at [Statuspage API Documentation](https://developer.statuspage.io/) to understand the available endpoints, authentication methods, and data structures. This will help you know what data you can access and how to retrieve it.

To access Statuspage data, you'll need to authenticate your requests. Obtain your API key from your Statuspage account under the API section. This typically involves creating an API token which you will use to authorize your API requests.

Decide which programming language you will use to interact with the API. Popular choices include Python, JavaScript, and Ruby. Set up your development environment by installing necessary tools. For Python, ensure you have `requests` library installed; for Node.js, `axios` or `node-fetch` can be used.

Write a script to make HTTP GET requests to the desired Statuspage API endpoints using the API token for authentication. For example, to retrieve incidents, you would make a request to the `/pages/{page_id}/incidents` endpoint. Ensure you handle pagination if the data set is large.

Example in Python:
```python
import requests

api_key = 'your_api_key'
page_id = 'your_page_id'
url = f'https://api.statuspage.io/v1/pages/{page_id}/incidents'
headers = {'Authorization': f'OAuth {api_key}'}

response = requests.get(url, headers=headers)
data = response.json()
```

After retrieving the data, you might need to transform it to fit your local JSON structure. This could involve selecting specific fields, renaming keys, or reformatting date strings. Use your programming language's data manipulation capabilities to achieve this.

Once the data is in the desired format, write it to a local JSON file. This can be done using built-in file handling and JSON libraries in your chosen language. Ensure that you handle any exceptions that might occur during file writing.

Example in Python:
```python
import json

with open('statuspage_data.json', 'w') as json_file:
json.dump(data, json_file, indent=4)
```

Finally, consider automating this process if you need to update your local JSON file regularly. Use a task scheduler like Cron on Unix-based systems or Task Scheduler on Windows to run your script at defined intervals.

By following these steps, you will be able to move data from Statuspage to a local JSON file without relying on third-party connectors or integrations.