Familiarize yourself with Asana's API documentation, which provides details on how to authenticate, request data, and understand the structure of the data returned. This is crucial for manually extracting data using HTTP requests.

Create an Asana Personal Access Token (PAT) to authenticate your requests. Go to your Asana account settings, navigate to the "Apps" section, and generate a PAT. Store this token securely as it will be used to authorize your API requests.

Determine which data you need from Asana, such as tasks, projects, or users. Identify the appropriate API endpoints that provide this data. For example, to retrieve tasks, you would use the `/tasks` endpoint.

Use a tool like `curl` or Postman to make HTTP GET requests to the selected Asana API endpoints. Include your Personal Access Token in the request header for authentication. For example, a curl command might look like: ```
curl -H "Authorization: Bearer YOUR_PERSONAL_ACCESS_TOKEN" "https://app.asana.com/api/1.0/tasks"
```

Once you receive the response from Asana, it will be in JSON format. Use a programming language like Python, JavaScript, or any other that you are comfortable with to parse this JSON. This will allow you to manipulate and format the data as needed.

Based on your requirements, transform the JSON data into the structure you need. This might include selecting specific fields, renaming keys, or reorganizing the data hierarchy. Use your programming language's JSON handling capabilities to achieve this.

After transforming the data, write it to a local JSON file. In Python, for instance, you can use the `json` module to write to a file:
```python
import json
with open('asana_data.json', 'w') as outfile:
json.dump(transformed_data, outfile, indent=4)
```
This will create a file named `asana_data.json` in your local directory containing the structured data from Asana.
By following these steps, you can manually move data from Asana to a local JSON file without relying on third-party tools or integrations.