First, ensure you have access to the Google Cloud Storage bucket containing your data. You need the appropriate permissions to read and download the data. Create a service account in your Google Cloud project and download the JSON key file. This key will be used to authenticate your requests to Google Cloud Storage.

You need to install the Google Cloud Storage and AWS SDKs in your development environment to interact with both services. Use pip to install the necessary packages for Python:
```bash
pip install google-cloud-storage boto3
```

Use the Google Cloud Storage client library to authenticate using the service account key and download the data to your local environment:
```python
from google.cloud import storage
# Set up client using the service account key
storage_client = storage.Client.from_service_account_json('path/to/your/service-account-key.json')
# Specify the bucket and the object you want to download
bucket_name = 'your-bucket-name'
source_blob_name = 'your-object-name'
destination_file_name = 'local-file-name'
bucket = storage_client.bucket(bucket_name)
blob = bucket.blob(source_blob_name)
blob.download_to_filename(destination_file_name)
```

Configure your AWS credentials to ensure your application can access DynamoDB. Save your AWS credentials in the `~/.aws/credentials` file or set environment variables for `AWS_ACCESS_KEY_ID` and `AWS_SECRET_ACCESS_KEY`.

Read the downloaded data file and transform it into a format suitable for DynamoDB. This typically involves converting data into JSON or a dictionary format if the data is in CSV or another structured format.
```python
import json
# Example for JSON data
with open('local-file-name', 'r') as file:
data = json.load(file)
# Transform or prepare your data as needed for DynamoDB
```

Use the AWS SDK (Boto3) to create a DynamoDB client and insert the data. If you haven't already, create a DynamoDB table where the data will be stored.
```python
import boto3
# Initialize a session using Amazon DynamoDB
dynamodb = boto3.resource('dynamodb', region_name='your-region')
# Select your table
table = dynamodb.Table('your-table-name')
# Insert data into the table
for item in data:
table.put_item(Item=item)
```

After the data transfer, verify that the data has been correctly inserted into DynamoDB by querying the table. This can be done using the AWS Management Console or by writing a small script to query the table and print the results.
```python
response = table.scan()
for item in response['Items']:
print(item)
```
By following these steps, you can successfully move data from Google Cloud Storage to DynamoDB without relying on third-party connectors or integrations.