To build a video chat room with Twilio Programmable Video and the Twilio Serverless Toolkit in JavaScript, start by setting up a Twilio account and installing the Twilio CLI. Create a new project using the `twilio serverless:init` command and add files for generating an access token and displaying the video preview screen. Write HTML to create buttons for joining and leaving the room, and JavaScript code to connect users to the room when they click "Join Room", disconnect them when they click "Leave Room", and display a remote participant's video. Finally, deploy the project using `twilio serverless:deploy` and share the URL with friends to use the video chat room.