To start, you need access to Clockify's API. Log into your Clockify account, navigate to the 'Profile' section, and locate your 'API Key'. This key will be used to authenticate API requests.

Prepare your local environment by ensuring you have a tool like cURL or a programming language such as Python or Node.js installed, which can make HTTP requests. This environment will allow you to interact with the Clockify API to fetch data.

Determine which data you need from Clockify (e.g., time entries, projects, users). Refer to the Clockify API documentation to identify the relevant endpoints for your data. Each endpoint will have specific paths, parameters, and methods (usually GET, for retrieving data).

Using your chosen tool or language, construct and execute HTTP GET requests to the Clockify API endpoints. Include your API key in the request headers for authentication. For example, using Python's `requests` library:

```python
import requests

headers = {'X-Api-Key': 'your_clockify_api_key'}
response = requests.get('https://api.clockify.me/api/v1/workspaces', headers=headers)

if response.status_code == 200:
data = response.json()
```

The response from the API will typically be in JSON format. Parse this data into a structure your code can work with, such as a dictionary or list in Python. This step ensures you can manipulate and filter the data as needed.

Organize the parsed data into the desired structure for your local JSON file. Consider which fields are necessary and how you want the data to be nested or structured. This might involve iterating through the data and creating a new dictionary or list that fits your needs.

```python
formatted_data = {
'projects': [], # Example structure
'time_entries': []
}
```

Once the data is formatted, write it to a local JSON file using a library like Python's `json`. Choose a suitable file name and ensure the file is saved in the appropriate directory.

```python
import json

with open('clockify_data.json', 'w') as outfile:
json.dump(formatted_data, outfile, indent=4)
```

By following these steps, you can successfully move data from Clockify to a local JSON file without relying on third-party connectors or integrations.