Begin by logging into your OneSignal account. Navigate to the dashboard where you can manage your apps. Choose the app from which you want to export the data.

Go to the "Settings" section of your selected app and find the "API & Keys" tab. Generate or retrieve your REST API key. This key is necessary for authenticating requests to OneSignal's API.

Visit OneSignal’s API documentation at https://documentation.onesignal.com/docs/using-our-api. Familiarize yourself with the endpoints that are relevant to the data you wish to export, such as those for fetching notifications, players, or outcomes.

Using a tool like cURL or Postman, construct a GET request to the relevant OneSignal API endpoint. Include the REST API key in the request header for authentication. For example, to fetch player data, you could use:
```
curl --include \
--request GET \
--header "Authorization: Basic YOUR_REST_API_KEY" \
"https://onesignal.com/api/v1/players?app_id=YOUR_APP_ID&limit=300"
```
Adjust query parameters as needed to refine the data you’re retrieving.

Execute the API request from your terminal or through a script. Capture the JSON response, which contains the data you need. Save this JSON data to a local file for the next step. Make sure to check the response for pagination if your data set exceeds the API’s limit per request.

Use a programming language like Python to convert the JSON data into a CSV format. Here is a simple example using Python:
```python
import json
import csv

# Load JSON data
with open('data.json') as json_file:
data = json.load(json_file)

# Specify the data fields you want to include
fields = ['id', 'identifier', 'session_count'] # Adjust fields as necessary

# Write to CSV
with open('data.csv', mode='w', newline='') as csv_file:
writer = csv.DictWriter(csv_file, fieldnames=fields)
writer.writeheader()
for item in data['players']: # Adjust based on your JSON structure
writer.writerow({field: item.get(field) for field in fields})
```

Open the generated CSV file using a spreadsheet application or a text editor to ensure that the data has been correctly transferred and formatted. Verify that all necessary fields are present and that the data integrity is maintained.

This guide provides a methodical approach to exporting data from OneSignal to a local CSV file using available tools and programming techniques, without relying on external integrations.