To access Twitter’s data, you need to create a Twitter Developer Account. Visit the Twitter Developer Platform, sign up for an account, and create a new application. This will provide you with API keys and tokens necessary to authenticate your requests to Twitter’s API.

Once your developer account is set up, navigate to the "Keys and Tokens" section of your app settings. Here, you will find your Consumer Key, Consumer Secret, Access Token, and Access Token Secret. These credentials are essential for accessing Twitter’s API programmatically.

On your local machine or server, install Python if it's not already installed. Use pip, Python’s package installer, to install the necessary libraries for interacting with Twitter and Elasticsearch. You'll primarily need `tweepy` for Twitter API interaction and `elasticsearch` for sending data to Elasticsearch.
```bash
pip install tweepy elasticsearch
```

Write a Python script to connect to Twitter’s API using the credentials obtained earlier. Use the `tweepy` library to authenticate and fetch tweets based on your criteria (e.g., by hashtag, user, etc.). For example, to fetch tweets containing a specific hashtag:
```python
import tweepy

auth = tweepy.OAuthHandler('CONSUMER_KEY', 'CONSUMER_SECRET')
auth.set_access_token('ACCESS_TOKEN', 'ACCESS_TOKEN_SECRET')
api = tweepy.API(auth)

# Example: Fetch tweets containing a specific hashtag
tweets = api.search_tweets(q="#example", count=100)
```

Install and configure Elasticsearch on your local machine or server. Ensure it’s running and accessible. You can download Elasticsearch from the official Elastic website and follow the installation instructions for your operating system. Once installed, start the Elasticsearch service.

Use the `elasticsearch` Python library to format the fetched tweets into JSON format suitable for Elasticsearch and index them. Establish a connection to your Elasticsearch instance and create an index if it doesn’t exist. Then, iterate over the fetched tweets and insert them into Elasticsearch.
```python
from elasticsearch import Elasticsearch

es = Elasticsearch([{'host': 'localhost', 'port': 9200}])

if not es.indices.exists(index="twitter_data"):
es.indices.create(index="twitter_data")

for tweet in tweets:
doc = {
'user': tweet.user.screen_name,
'text': tweet.text,
'created_at': tweet.created_at
}
es.index(index="twitter_data", body=doc)
```

Finally, verify that your data has been correctly indexed in Elasticsearch. You can do this by querying Elasticsearch directly. Use tools like Kibana (if available) for a user-friendly interface, or use a simple Python script to print indexed documents.
```python
res = es.search(index="twitter_data", body={"query": {"match_all": {}}})
for hit in res['hits']['hits']:
print(hit["_source"])
```

By following these steps, you can fetch Twitter data and index it into Elasticsearch without relying on any third-party connectors or integrations.