To start, you need to have access to the Pexels API. Visit the [Pexels API website](https://www.pexels.com/api/) and sign up for an account if you haven't already. Once registered, navigate to the API section to obtain your unique API key, which will be used to authenticate your requests.

Ensure you have Python installed on your machine. You will need the `requests` library to make HTTP requests and `csv` for writing data to a CSV file. Install the `requests` library using pip if you haven't done so:
```bash
pip install requests
```

Use Python to send a request to the Pexels API. You can start with a simple GET request to fetch data (e.g., a collection of photos). Here's a basic example of how to request data:
```python
import requests

API_KEY = 'YOUR_PEXELS_API_KEY'
headers = {'Authorization': API_KEY}
url = 'https://api.pexels.com/v1/search?query=nature&per_page=10'

response = requests.get(url, headers=headers)
data = response.json()
```

Once you have the JSON response from the API, parse it to extract the relevant data fields that you wish to store in the CSV. For instance, you might want to extract the photo URLs, photographer names, etc.
```python
photos = data['photos']
extracted_data = []

for photo in photos:
photo_data = {
'id': photo['id'],
'url': photo['url'],
'photographer': photo['photographer'],
'src': photo['src']['original']
}
extracted_data.append(photo_data)
```

Set up your CSV file structure by defining the headers that correspond to the data fields you've extracted. This ensures that each piece of information is correctly placed in your CSV file.
```python
import csv

csv_headers = ['id', 'url', 'photographer', 'src']
```

Open a file in write mode and use the `csv` module to write the headers and data rows into the CSV file. Ensure you handle file opening and closing properly to avoid data corruption.
```python
with open('pexels_data.csv', mode='w', newline='') as file:
writer = csv.DictWriter(file, fieldnames=csv_headers)
writer.writeheader()
writer.writerows(extracted_data)
```

After writing to the CSV, open the file to verify that the data has been correctly written. Check for any discrepancies and ensure the format matches your expectations. This step helps confirm the integrity and accuracy of the data transfer.

By following these steps, you can successfully transfer data from the Pexels API to a local CSV file without using any third-party connectors or integrations.