To add custom video call backgrounds to a Daily Prebuilt call frame in a vanilla JavaScript web app, developers can create a free Daily account and room, clone the demo repository, replace the placeholder room URL, install dependencies, and run the app. The app embeds a Daily Prebuilt call frame onto a page and shows a set of custom video backgrounds for the call participant to pick from. To populate the background options, a new function `initBackgrounds()` is called when the DOM has loaded, which loads the background images and sets up an event handler for the "reset" button. The `updateInputSettings()` API method is used to update and reset the video background, allowing developers to add custom backgrounds or remove the default one.