First, ensure that you have an AWS account. Access the AWS Management Console and create an IAM user with the necessary permissions to access DynamoDB. Note the AWS Access Key ID and Secret Access Key, as they will be required for programmatic access.

In the AWS Management Console, navigate to DynamoDB and create a new table. Define the primary key (hash key and optionally a range key) based on the data structure you plan to store. For example, you might use a URL as the primary key if you are storing performance data for different web pages.

Visit the [Google Cloud Console](https://console.cloud.google.com/), create a new project or select an existing one, and navigate to the API & Services section. Enable the PageSpeed Insights API and create credentials to obtain an API key. This key will be used to authenticate requests.

Create a script using a programming language like Python. Use the `requests` library to send HTTP requests to the PageSpeed Insights API, passing in your API key and the URL of the page you want to analyze. Parse the JSON response to extract the performance data you need.

```python
import requests

def fetch_data(api_key, url):
response = requests.get(
f"https://www.googleapis.com/pagespeedonline/v5/runPagespeed?url={url}&key={api_key}"
)
data = response.json()
return data
```

Process the JSON data retrieved from the API to match the schema of your DynamoDB table. This may involve extracting specific metrics or transforming the data format. Ensure that the data is structured according to the primary key and attributes you defined in your DynamoDB table.

```python
def process_data(raw_data):
processed_data = {
'url': raw_data['id'], # Assuming 'id' contains the URL
'performance_score': raw_data['lighthouseResult']['categories']['performance']['score']
# Add more fields as needed
}
return processed_data
```

Use the AWS SDK (such as Boto3 for Python) to programmatically insert the processed data into your DynamoDB table. Initialize a DynamoDB client with your AWS credentials and use the `put_item` method to add data.

```python
import boto3

def store_data(dynamodb_table, data):
dynamodb = boto3.resource('dynamodb', region_name='your-region', aws_access_key_id='your-access-key', aws_secret_access_key='your-secret-key')
table = dynamodb.Table(dynamodb_table)
table.put_item(Item=data)
```

To automate data fetching and storage, set up a cron job or a scheduled task that runs your script at desired intervals. This can be done on your local machine, an EC2 instance, or by using AWS Lambda with a CloudWatch Events rule for scheduling. Ensure the environment where your script runs has network access to both Google APIs and AWS services.

Following these steps, you can efficiently move data from Google PageSpeed Insights to DynamoDB using custom scripts and AWS services without relying on third-party connectors or integrations.