Begin by visiting the Pivotal Tracker website and logging in with your credentials. Ensure you have access to the appropriate project(s) from which you want to export data.

Once logged in, navigate to the specific project dashboard that contains the data you wish to export. Ensure you have the necessary permissions to view and export data from this project.

Click on your profile icon in the top-right corner and select 'Profile' from the dropdown menu. Scroll down to find your API token, which will be used for authentication in API requests. Copy this token for later use.

Open a terminal or command prompt on your local machine. Use the `curl` command to make an API request to Pivotal Tracker. Replace `YOUR_API_TOKEN` with your actual API token and `YOUR_PROJECT_ID` with the project ID from which you are exporting data:
```bash
curl -X GET "https://www.pivotaltracker.com/services/v5/projects/YOUR_PROJECT_ID/stories" -H "X-TrackerToken: YOUR_API_TOKEN" -H "Content-Type: application/json" -o pivotal_data.json
```
This command fetches all stories from the specified project and saves them to a file named `pivotal_data.json`.

The data fetched from the API will be in JSON format. Use a script to convert this JSON data into a CSV file. You can write a Python script to achieve this. Save the following script as `json_to_csv.py`:

```python
import json
import csv

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

# Specify the CSV file to write to
csv_file = open('pivotal_data.csv', mode='w', newline='', encoding='utf-8')
csv_writer = csv.writer(csv_file)

# Write headers
headers = list(data[0].keys())
csv_writer.writerow(headers)

# Write data rows
for story in data:
csv_writer.writerow(story.values())

# Close CSV file
csv_file.close()
```

Execute the Python script to convert the JSON file to a CSV file. Ensure that Python is installed on your system. Run the script using the following command:
```bash
python json_to_csv.py
```
This will generate a `pivotal_data.csv` file in your current directory.

Open the `pivotal_data.csv` file with a spreadsheet application like Microsoft Excel or Google Sheets to verify the data. Check that all necessary fields have been exported correctly and that the data is formatted as needed.

By following these steps, you can effectively move data from Pivotal Tracker to a local CSV file without using third-party connectors or integrations.