Begin by ensuring you have access to the Azure Table Storage account where your data resides. You'll need the account name and the account key to access the data programmatically. Verify that your Azure Storage Table contains the data that you want to move to Google Pub/Sub.

In your Google Cloud Platform (GCP) console, create a new service account that will be used to authenticate your requests to Google Pub/Sub. Assign the necessary roles to this service account, such as `Pub/Sub Publisher`, to allow it to publish messages to a Pub/Sub topic.

After creating the service account, generate a JSON key for it. This key will be used in your script to authenticate your requests to Google Pub/Sub. Store this JSON key file securely, as it contains sensitive information.

Install Python on your local machine or server if you haven't done so already. You will also need to install the Azure and Google Cloud SDKs for Python. This can be done using pip:
```bash
pip install azure-storage azure-core google-cloud-pubsub
```

Write a Python script to connect to your Azure Table Storage and extract the data. Use the Azure Storage SDK to authenticate and retrieve data from your table. Here is a basic template to get you started:
```python
from azure.data.tables import TableServiceClient

connection_string = "DefaultEndpointsProtocol=https;AccountName=;AccountKey=;EndpointSuffix=core.windows.net"
table_service = TableServiceClient.from_connection_string(conn_str=connection_string)
table_client = table_service.get_table_client(table_name="")

# Fetch all entities
entities = table_client.list_entities()
```

Extend your Python script to include functionality for publishing data to Google Pub/Sub. Use the Pub/Sub client library to authenticate using the JSON key file and publish messages to your topic:
```python
from google.cloud import pubsub_v1
import json

# Set up Pub/Sub client
publisher = pubsub_v1.PublisherClient.from_service_account_json('')
topic_path = publisher.topic_path('', '')

# Publish entities to Pub/Sub
for entity in entities:
message_data = json.dumps(entity).encode('utf-8')
publisher.publish(topic_path, data=message_data)
```

Run your Python script to execute the data transfer from Azure Table Storage to Google Pub/Sub. Monitor the process for any errors or exceptions and ensure that all data is successfully published to your Pub/Sub topic. Check both Azure Table Storage and Google Pub/Sub to verify that the data transfer is complete and accurate. Adjust your script as necessary based on any specific requirements or data formatting needs.