Before accessing OpenWeather's data, you need an API key. Visit the OpenWeather website, sign up for a free account, and navigate to the API section. Generate and note down your API key, as you'll need it to authenticate your requests.

Determine which specific data you need from OpenWeather. This could include current weather data, forecasts, or historical data. Familiarize yourself with the OpenWeather API documentation to understand the available endpoints and parameters.

Formulate an HTTP GET request to retrieve the data you need. The request URL will typically include the endpoint, query parameters such as location coordinates or city name, and your API key. For example:
```
http://api.openweathermap.org/data/2.5/weather?q=London&appid=YOUR_API_KEY
```
Replace `YOUR_API_KEY` with your actual API key.

Use a programming language like Python to send the HTTP request. Utilize libraries such as `requests` to make the process easier. Here's a basic example in Python:
```python
import requests

url = "http://api.openweathermap.org/data/2.5/weather?q=London&appid=YOUR_API_KEY"
response = requests.get(url)
data = response.json()
```

Once you receive a response, it will typically be in JSON format. Parse this JSON data to extract the specific information you need. Python's `json` module can be used to manipulate this data easily.

After extracting the relevant information, structure it in a format suitable for JSON storage. This might involve creating a dictionary or list in Python that mirrors the desired JSON structure.

Finally, write the formatted data to a local JSON file. Use Python's `json.dump()` method to serialize the data. Here's how you can do it:
```python
import json

with open('weather_data.json', 'w') as json_file:
json.dump(data, json_file, indent=4)
```
This will save the data to a file named `weather_data.json` in your current working directory, with indentation for readability.

By following these steps, you can effectively retrieve data from OpenWeather and store it locally in a JSON file without the need for third-party connectors or integrations.