Begin by familiarizing yourself with the SpaceX API documentation, available at `https://github.com/r-spacex/SpaceX-API`. This will help you understand the available endpoints, request methods, and data structure. Identify the specific data you need, such as launch details, rockets, or capsules.

Ensure you have a working Python environment on your local machine. Install Python if you haven’t already. You can download it from `https://www.python.org/`. Additionally, ensure you have the `requests` and `csv` libraries, which are usually included with Python by default, but you can install them using pip if needed (e.g., `pip install requests`).

Use Python to make a request to the SpaceX API. Here’s a basic example:
```python
import requests

url = 'https://api.spacexdata.com/v4/launches'
response = requests.get(url)

if response.status_code == 200:
data = response.json()
else:
raise Exception(f"Error fetching data: {response.status_code}")
```
This code fetches data from the SpaceX API's launches endpoint and stores it in a variable if the request is successful.

Analyze the JSON data structure obtained from the API to determine which fields you need. Extract these fields and prepare them for writing to a CSV file. For example:
```python
launches = []
for launch in data:
launches.append({
'name': launch['name'],
'date': launch['date_utc'],
'success': launch['success'],
'rocket_id': launch['rocket']
})
```

Use the `csv` module to write the processed data to a CSV file. Here’s an example:
```python
import csv

with open('spacex_launches.csv', mode='w', newline='') as file:
writer = csv.DictWriter(file, fieldnames=['name', 'date', 'success', 'rocket_id'])
writer.writeheader()
writer.writerows(launches)
```
This script creates a CSV file named 'spacex_launches.csv' and writes the extracted data into it.

Once the CSV file is created, open it using a spreadsheet application like Excel or a text editor to ensure the data is correctly formatted and complete. Check for consistency and accuracy in what is written compared to the original API data.

If you need to regularly update the CSV file with new data, consider automating the script using a task scheduler. On Windows, you can use Task Scheduler, and on macOS or Linux, use cron jobs. This will allow your script to run at specified intervals without manual intervention.

By following these steps, you can efficiently move data from the SpaceX API to a local CSV file without relying on third-party connectors or integrations.