Begin by setting up a Kafka environment. This involves installing Apache Kafka on your server. Download the Kafka binaries from the official Apache Kafka website, and follow the installation guide to set up a Kafka broker. Ensure you have Java installed, as Kafka runs on the JVM. Start the Zookeeper server followed by the Kafka broker using the provided scripts in the Kafka installation directory.

Once Kafka is up and running, create a topic to which you will publish the news data. Use the Kafka command-line tool to create a topic. For example, execute `bin/kafka-topics.sh --create --topic news-topic --bootstrap-server localhost:9092 --partitions 1 --replication-factor 1` in your terminal. This command creates a topic named "news-topic" with one partition and a replication factor of one.

Use a programming language such as Python to fetch data from the News API. First, sign up for the News API service to get your API key. Then, using Python's `requests` library, make GET requests to the News API endpoint with your API key to retrieve the latest news articles. Parse the JSON response to extract the relevant data you wish to send to Kafka.

Develop a Kafka producer application to send data to the Kafka topic. Using the `kafka-python` library, set up a producer in Python. Initialize the producer with the Kafka broker's address. For example:
```python
from kafka import KafkaProducer
import json

producer = KafkaProducer(
bootstrap_servers='localhost:9092',
value_serializer=lambda v: json.dumps(v).encode('utf-8')
)
```

Loop through the news data retrieved from the News API, and for each news article, transform it into the desired format (e.g., JSON). Use the Kafka producer to send this data to your Kafka topic. For example:
```python
for article in news_data['articles']:
producer.send('news-topic', article)
```

Implement error handling and logging to make your data pipeline robust. Use try-except blocks to catch exceptions during data fetching and sending. Log these errors using Python's `logging` module to ensure you can diagnose issues later. This step ensures any network or data-related errors are captured and handled appropriately.

Finally, test your data pipeline to ensure it's working correctly. Consume messages from Kafka using a simple consumer to verify that the data is being received as expected. Use Kafka's consumer shell script or write a small consumer program. Additionally, monitor the Kafka server and topics using Kafka's built-in tools and ensure the system's health and performance are optimal.

By following these steps, you can effectively move data from the News API into Kafka without relying on any third-party connectors or integrations.