Begin by accessing the Datadog API. You need to have an API key and an application key, which you can generate from the Datadog dashboard under the API section. These keys will allow you to authenticate and access data programmatically via the API.

Familiarize yourself with the specific API endpoint you need to retrieve the data you want. Datadog provides various endpoints for metrics, logs, and other data types. Review the Datadog API documentation to determine the appropriate endpoint and the parameters you need to include in your API request.

Write a script in a programming language such as Python to fetch the data from Datadog. Use the `requests` library to send HTTP requests to the Datadog API endpoint. Make sure to include the API key and application key for authentication in the request headers.

Example in Python:
```python
import requests

# Define your Datadog API and App keys
api_key = 'YOUR_DATADOG_API_KEY'
app_key = 'YOUR_DATADOG_APP_KEY'

# API endpoint URL
url = 'https://api.datadoghq.com/api/v1/your_endpoint'

# Headers for authentication
headers = {
'DD-API-KEY': api_key,
'DD-APPLICATION-KEY': app_key
}

# Send the request
response = requests.get(url, headers=headers)

# Parse the JSON response
data = response.json()
```

Once you have fetched the data, process and format it as needed for Google Sheets. This may involve filtering the data, restructuring it, or transforming it into a tabular format suitable for a spreadsheet.

Enable the Google Sheets API through the Google Cloud Console. Create a new project and enable the Google Sheets API. Then, create credentials (OAuth 2.0 Client ID) and download the JSON credentials file. This file will be used to authenticate your script to access Google Sheets.

Use the Google Sheets API to write data to a Google Sheet. Install the `gspread` library in Python to facilitate this process. Authenticate using the credentials you set up and open or create a new Google Sheet to write the data.

Example in Python:
```python
import gspread
from oauth2client.service_account import ServiceAccountCredentials

# Define the scope
scope = ["https://spreadsheets.google.com/feeds", "https://www.googleapis.com/auth/drive"]

# Authenticate and construct the service
credentials = ServiceAccountCredentials.from_json_keyfile_name('path/to/credentials.json', scope)
client = gspread.authorize(credentials)

# Open the Google Sheet
sheet = client.open('Your Google Sheet Name').sheet1

# Write data to the sheet
for i, row in enumerate(data):
sheet.insert_row(row, i + 1)
```

To keep the data updated, automate the script to run at regular intervals using a task scheduler such as cron (on Linux or macOS) or Task Scheduler (on Windows). This will ensure that your Google Sheets data remains in sync with Datadog without manual intervention.

By following these steps, you can effectively move data from Datadog to Google Sheets without relying on third-party connectors or integrations.