First, ensure you have the necessary software installed on your machine. You will need Python (version 3.6 or newer), pip (Python's package installer), and MongoDB. You can download Python from the official website and MongoDB from its official site. Once Python is installed, you can install the necessary libraries by running `pip install pymongo requests` in your terminal or command prompt.

Sign up for an account on the news API provider's website to obtain your API key. This key will be required to authenticate your requests to the news API. Keep this key secure and do not expose it publicly.

Create a Python script that sends a request to the news API and retrieves the data. Use the `requests` library to make HTTP requests. Here's an example of how to fetch data:

```python
import requests

api_key = 'your_api_key'
url = f'https://newsapi.org/v2/top-headlines?country=us&apiKey={api_key}'

response = requests.get(url)
data = response.json()
articles = data.get('articles', [])
```

This script fetches the top headlines from the US. You can customize the URL to suit your needs, such as fetching news by category or source.

Start your MongoDB server. Open a new terminal or command prompt and run `mongod` to start the MongoDB server. Then, open another terminal and use the `mongo` shell to create a database and a collection where you will store the news articles:

```bash
mongo
use newsdb
db.createCollection('articles')
```

Modify your Python script to include code that connects to your MongoDB database and inserts the fetched articles. Use the `pymongo` library to interact with MongoDB:

```python
from pymongo import MongoClient

client = MongoClient('localhost', 27017)
db = client.newsdb
articles_collection = db.articles

if articles:
articles_collection.insert_many(articles)
print(f'Inserted {len(articles)} articles into MongoDB.')
else:
print('No articles to insert.')
```

Enhance your script by adding error handling to manage potential errors that may occur during the HTTP request or database operations. Use try-except blocks to catch and handle exceptions:

```python
try:
response = requests.get(url)
response.raise_for_status()
data = response.json()
articles = data.get('articles', [])
except requests.exceptions.RequestException as e:
print(f'Error fetching data: {e}')
```

Similarly, wrap your MongoDB operations in a try-except block to handle database-related errors.

Test your script to ensure it works as expected. Run the script manually at first to check that data is correctly fetched and stored. Once verified, consider automating the process using cron jobs (on Unix-based systems) or Task Scheduler (on Windows) to run your script at regular intervals.

By following these steps, you can successfully move data from a news API to a MongoDB database without relying on third-party connectors or integrations.