The Vonage Messages API Sandbox allows users to test and develop automated services for Facebook Messenger without leaving their web presence on Facebook. To set up a quick service, developers need to create a server using Node.js, Express.js, body-parser, and axios, and configure the middleware to listen on port 3000. The server needs to be publicly available, which can be done with ngrok or Glitch. Developers also need to obtain API credentials and the sandbox Messenger ID from the cURL command on the sandbox page. Once the server is set up, developers can send messages using axios and receive incoming messages by listening for a received message first. The endpoint responds with a confirmation of what was sent. With this setup, developers can now build a reply to their user and try it out with a whitelisted Messenger client.