To create a "Dial-a-Carol" service using Nexmo and Vonage APIs, users need to set up a virtual phone number, configure webhooks, and use Python code to handle incoming calls. The code uses Flask to create a web application that interacts with Nexmo's API to play Christmas carols when a user dials in. The application sets up an answer webhook to send the option menu to the user, and a DTMF webhook to receive the user's input, which is then used to select a carol from a predefined list. Once set up, users can dial into Nexmo using their assigned number, make a selection, and listen to a festive carol. The code includes detailed explanations of how the webhooks work, as well as resources for further exploration.