Begin by signing up for an account on News API's website. Once registered, navigate to the API keys section to generate your unique API key. This key will be used to authenticate your requests when fetching data from the News API.

Install Python if it is not already installed on your system. Set up a virtual environment to keep your dependencies organized. You can do this using `python -m venv env` and then activate it. Install necessary packages by running `pip install requests` to handle HTTP requests.

Write a Python script to make HTTP GET requests to the News API endpoint. Use the `requests` library to fetch data. Construct your API request URL using the API key and the parameters for the type of news data you need. For example, to get the latest headlines:
```python
import requests

url = 'https://newsapi.org/v2/top-headlines'
params = {
'country': 'us',
'apiKey': 'YOUR_API_KEY'
}
response = requests.get(url, params=params)
data = response.json()
```

Inspect the JSON response from the News API and determine the structure of the data. Extract the relevant fields you need, such as `title`, `description`, `url`, etc. Clean the data to ensure it’s in the correct format for Convex. This might include removing duplicates or handling missing values.

Create an account on Convex and set up a new project. Obtain your Convex project URL and authentication credentials. Ensure you have the necessary permissions to write data to your Convex database.

Prepare the data for insertion into Convex by converting it into a format that Convex can accept. Typically, this means ensuring your data is structured as a dictionary or JSON object. You might need to map fields from the News API response to your Convex schema.

Use the Convex HTTP API to insert the data. Make an HTTP POST request to your Convex project endpoint with the processed data. You can use the `requests` library again to send this data:
```python
import requests

convex_url = 'https://your-convex-endpoint/api/your-database'
headers = {
'Authorization': 'Bearer YOUR_CONVEX_TOKEN',
'Content-Type': 'application/json'
}
response = requests.post(convex_url, headers=headers, json=your_data)
if response.status_code == 200:
print("Data successfully inserted into Convex.")
else:
print("Failed to insert data into Convex:", response.text)
```

By following these steps, you can effectively move data from the News API to Convex without relying on third-party connectors or integrations. Adjust the specifics according to your data structure and requirements.