First, visit the Weatherstack website and sign up for an account to obtain an API key. This key will allow you to authenticate your requests to the Weatherstack API and access the weather data.

Familiarize yourself with the Weatherstack API documentation. Pay close attention to the endpoints available, the parameters you need to specify (such as location and type of data), and the format of the response (typically JSON).

Set up your local environment by installing Python if you haven't already. You will also need to install necessary libraries such as `requests` for handling HTTP requests and `csv` for writing data to CSV files. You can install `requests` using pip:
```bash
pip install requests
```

Write a Python script to fetch data from the Weatherstack API. Use the `requests` library to make GET requests to the API endpoint. Pass your API key and necessary parameters in the request URL. Here is a sample script:
```python
import requests

api_key = 'your_api_key'
location = 'New York'
url = f'http://api.weatherstack.com/current?access_key={api_key}&query={location}'

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

Once you receive the response, parse the JSON data to extract the necessary weather information. This might include temperature, humidity, wind speed, etc. You can access these using standard Python dictionary operations. For example:
```python
temperature = data['current']['temperature']
humidity = data['current']['humidity']
wind_speed = data['current']['wind_speed']
```

Use Python's built-in `csv` module to write the extracted data to a CSV file. Open a file in write mode and use `csv.writer` to write headers followed by your data rows. Here's a sample code snippet:
```python
import csv

with open('weather_data.csv', mode='w', newline='') as file:
writer = csv.writer(file)
# Write headers
writer.writerow(['Location', 'Temperature', 'Humidity', 'Wind Speed'])
# Write data
writer.writerow([location, temperature, humidity, wind_speed])
```

If you want to regularly update the data, consider automating the script execution. You can use task schedulers like cron in Unix-based systems or Task Scheduler in Windows to run your script at regular intervals.

By following these steps, you can effectively retrieve weather data from Weatherstack and store it locally in a CSV file without relying on third-party connectors.