Sign up for a free account on the Alpha Vantage website (https://www.alphavantage.co). After registration, you'll receive an API key, which is essential for accessing the financial data.

Familiarize yourself with the Alpha Vantage API documentation to understand the available endpoints and parameters. This will include the function names (e.g., TIME_SERIES_INTRADAY), required parameters (like symbol, interval), and optional parameters.

Formulate the correct API request URL using your API key and desired parameters. For example, to fetch intraday time series data for a stock symbol (e.g., IBM), your URL might look like:
```
https://www.alphavantage.co/query?function=TIME_SERIES_INTRADAY&symbol=IBM&interval=5min&apikey=YOUR_API_KEY
```
Replace `YOUR_API_KEY` with your actual API key.

Use a programming language such as Python to send a GET request to the API endpoint. For example, in Python, you can use the `requests` library:
```python
import requests

url = "https://www.alphavantage.co/query?function=TIME_SERIES_INTRADAY&symbol=IBM&interval=5min&apikey=YOUR_API_KEY"
response = requests.get(url)
data = response.json()
```

Extract the relevant data from the JSON response. Alpha Vantage typically provides data under specific keys. For instance, in the intraday endpoint, the data might be under a key like `"Time Series (5min)"`. You'll need to loop through this data to extract the information you need.

Organize the parsed data into a format suitable for CSV. This involves creating a list of dictionaries or a list of lists where each sublist or dictionary represents a row in the CSV file. Ensure you include headers (e.g., timestamp, open, high, low, close, volume).

Finally, use a CSV library to write the data to a file. In Python, you can use the built-in `csv` module:
```python
import csv

with open('alpha_vantage_data.csv', mode='w', newline='') as file:
writer = csv.writer(file)
# Write the header
writer.writerow(["timestamp", "open", "high", "low", "close", "volume"])
# Write the data rows
for timestamp, values in data["Time Series (5min)"].items():
row = [timestamp, values['1. open'], values['2. high'], values['3. low'], values['4. close'], values['5. volume']]
writer.writerow(row)
```
This will save the fetched data to `alpha_vantage_data.csv` in the current working directory. Adjust the file name and path as needed.