ColdFusion developers can use the Twilio REST API to initiate calls. To start, replace placeholders with actual account information, such as an account SID, secret key, caller ID, called phone number, and URL to execute. Next, create a ColdFusion HTTP request using these parameters and send it to the Twilio API. The response will contain details about the initiated call, which can be displayed in the application. This process allows developers to integrate voice calls into their ColdFusion applications.