To set up a conference call using Nexmo, developers need to create a Vonage API account, purchase a virtual phone number, and add the Nexmo PHP library as a dependency. They then write an `answer.php` file that returns a Nexmo Call Control Object (NCCO) to instruct how incoming calls should be handled, including a "talk" action for a greeting and a "conversation" action to join the conference call. The NCCO is returned with a Content-Type header set to application/json. Developers can test their code by starting a PHP webserver from the `public/` directory and making requests to the `answer.php` endpoint using an HTTP client. To make the code publicly available, developers can use tools like Ngrok to expose their local development platform. They then create an application with a webhook endpoint for incoming calls, link it to the purchased virtual phone number, and handle call events by writing an event handler in PHP. Once set up, developers can join conference calls using the Nexmo number and see the events arriving at the `event.php` endpoint.