First, ensure that Elasticsearch is installed and running on your local machine or server. You can download it from the [official Elasticsearch website](https://www.elastic.co/downloads/elasticsearch). Follow the installation instructions specific to your operating system. Start Elasticsearch by running the `bin/elasticsearch` command from the installation directory.

Register for an API key from the News API provider you intend to use (e.g., NewsAPI.org). This key will be necessary for authenticating your requests. Familiarize yourself with the API documentation to understand the endpoints and parameters available for fetching news data.

Write a script in a programming language of your choice (such as Python) to make HTTP GET requests to the News API. Utilize libraries like `requests` in Python to send requests and fetch data. Ensure your script handles pagination if the API returns data in pages. Here's a basic example in Python:

```python
import requests

API_KEY = 'your_news_api_key'
URL = 'https://newsapi.org/v2/everything'
PARAMS = {
'q': 'technology',
'apiKey': API_KEY,
'pageSize': 100
}

response = requests.get(URL, params=PARAMS)
news_data = response.json().get('articles', [])
```

Transform the fetched data into a format suitable for Elasticsearch. Typically, this means ensuring each news article has a structured JSON format with fields that Elasticsearch can index. Consider fields like `title`, `description`, `content`, `author`, `publishedAt`, and `source`. Validate and clean the data to remove any inconsistencies or null values.

Use the Elasticsearch REST API to index the transformed news data. Create an index (e.g., `news`) if it does not exist. For each article, send an HTTP POST request to the Elasticsearch `_bulk` API endpoint for efficient data indexing. Here's an example in Python:

```python
from elasticsearch import Elasticsearch

es = Elasticsearch()

def index_data(news_data):
actions = [
{"index": {"_index": "news", "_id": article.get('url')}},
article
for article in news_data
]

es.bulk(index='news', body=actions)

index_data(news_data)
```

If you want to automate the data fetching and indexing process, consider setting up a cron job (on Linux) or a scheduled task (on Windows) to run your script at regular intervals. This ensures your Elasticsearch index is continually updated with the latest news articles.

Regularly monitor your Elasticsearch instance to ensure smooth operation. Use Elasticsearch's built-in tools to check index health, performance, and storage requirements. Make adjustments as necessary, such as optimizing index settings or scaling your Elasticsearch cluster if handling large volumes of data.

By following these steps, you can efficiently move data from a News API to an Elasticsearch destination without relying on third-party connectors or integrations.