First, obtain access to the Google PageSpeed Insights API. Visit the Google Developer Console, create a new project, and enable the PageSpeed Insights API. Generate an API key that will be used to authenticate your requests.

Formulate the URL for the API call. The basic structure is `https://www.googleapis.com/pagespeedonline/v5/runPagespeed?url=YOUR_URL&key=YOUR_API_KEY`. Replace `YOUR_URL` with the website you want to analyze and `YOUR_API_KEY` with the API key obtained in step 1.

Use a programming language such as Python to make a request to the API. Utilize the `requests` library to send a GET request to the URL you constructed. Here's a basic Python code snippet:
```python
import requests

url = 'https://www.googleapis.com/pagespeedonline/v5/runPagespeed'
params = {
'url': 'YOUR_URL',
'key': 'YOUR_API_KEY'
}
response = requests.get(url, params=params)
data = response.json()
```

Extract the relevant data from the JSON response. The response contains various metrics like performance score, first contentful paint, speed index, etc. Identify the data points you need for your CSV:
```python
metrics = {
'performance_score': data['lighthouseResult']['categories']['performance']['score'],
'first_contentful_paint': data['lighthouseResult']['audits']['first-contentful-paint']['displayValue'],
'speed_index': data['lighthouseResult']['audits']['speed-index']['displayValue']
}
```

Organize the parsed data into a format suitable for CSV. Create a list of dictionaries where each dictionary represents a row in the CSV file. For example:
```python
csv_data = [metrics]
```

Use the `csv` module in Python to write the organized data to a CSV file. Specify the fieldnames and use `DictWriter` to handle writing the data:
```python
import csv

with open('pagespeed_data.csv', mode='w', newline='') as file:
writer = csv.DictWriter(file, fieldnames=metrics.keys())
writer.writeheader()
writer.writerows(csv_data)
```

After writing to the CSV, open the file to ensure that all data has been accurately recorded. Check for correct headers and data entries to confirm the process was successful.

By following these steps, you can efficiently transfer data from Google PageSpeed Insights to a CSV file without relying on third-party tools.