Start by accessing the Gutendex API to retrieve the data you need. Open your web browser and navigate to the Gutendex API endpoint, typically found at `https://gutendex.com/books`, or refer to their documentation for the correct URL. This endpoint will allow you to query book data in JSON format.

Use a Python script to fetch data from the Gutendex API. Open your Python environment and use the `requests` library to send a GET request to the API. For example:
```python
import requests

response = requests.get('https://gutendex.com/books')
data = response.json()
```

Process the JSON response to extract the data fields you need. Determine which attributes (e.g., title, author) you want to transfer to Google Sheets, and filter the JSON data accordingly.
```python
books = data['results']
extracted_data = [(book['title'], book['author']) for book in books]
```

Convert the extracted data into a format compatible with Google Sheets. Typically, you would format it as a list of lists or a 2D array, where each inner list represents a row of data.
```python
formatted_data = [["Title", "Author"]] # Header row
formatted_data.extend(extracted_data)
```

Create a new Google Sheet or open an existing one where you want to import the data. Ensure you have edit access to this sheet. Note the sheet's name and the range where you want to insert the data (e.g., `Sheet1!A1`).

Set up authentication for the Google Sheets API using the `gspread` and `oauth2client` libraries in Python. Follow these steps:
- Enable the Google Sheets API in your Google Cloud Console.
- Create and download a service account JSON key.
- Share the Google Sheet with the email from the service account.
- Authenticate using the downloaded JSON key.
```python
import gspread
from oauth2client.service_account import ServiceAccountCredentials

scope = ["https://spreadsheets.google.com/feeds", "https://www.googleapis.com/auth/drive"]
creds = ServiceAccountCredentials.from_json_keyfile_name('path/to/your/json/keyfile.json', scope)
client = gspread.authorize(creds)
```

Use the authenticated client to open your Google Sheet and insert the formatted data at the specified range.
```python
sheet = client.open("Your Google Sheet Name").sheet1
sheet.update('A1', formatted_data)
```

By following these steps, you can transfer data from Gutendex to Google Sheets without relying on third-party connectors or integrations, using only Python and appropriate libraries.