First, familiarize yourself with Docker Hub's API by visiting the Docker Hub documentation. You will need to access data such as repository details using the API. Ensure you have your Docker Hub account credentials ready, as some API endpoints may require authentication.

If authentication is required, generate an access token or use your Docker Hub username and password to access the API. This will allow you to fetch private repository data if necessary. Note down your credentials securely.

Write a script in a programming language like Python to send HTTP requests to Docker Hub's API. Use the `requests` library to simplify HTTP requests. Retrieve the data you need, such as repository details, tags, or image sizes. Store this data in a structured format like JSON.

```python
import requests

# Example of fetching repository data
response = requests.get('https://hub.docker.com/v2/repositories/{username}/{repository}/tags')
data = response.json() # Store the JSON response
```

Process the fetched JSON data to extract the required information. Convert this data into a structured format, such as a list of dictionaries, that can be easily written to a CSV file. Ensure that each element represents a row of data.

```python
# Example of processing JSON data
tag_data = [{"name": tag["name"], "last_updated": tag["last_updated"]} for tag in data['results']]
```

Use Python’s `csv` library to write the structured data to a CSV file. This file will serve as an intermediary step to transfer data from Docker Hub to Google Sheets.

```python
import csv

with open('docker_data.csv', mode='w', newline='') as file:
writer = csv.DictWriter(file, fieldnames=["name", "last_updated"])
writer.writeheader()
writer.writerows(tag_data)
```

Manually upload the CSV file to your Google Drive. This step doesn’t require any third-party tools or integrations, but you need to have access to your Google Drive account and ensure the file is correctly uploaded.

Open Google Sheets and create a new spreadsheet. Use the 'File > Import' functionality to import the CSV file from your Google Drive into the Google Sheet. Choose the correct options to ensure that data is imported as you desire (e.g., separator type, import location within the sheet).

By following these steps, you can effectively transfer data from Docker Hub into Google Sheets without using third-party connectors or integrations.