JavaScript can display output in HTML elements using innerHTML, in the HTML output using document.write(), in alert boxes using window.alert(), and in the browser console using console.log(). It demonstrates writing the result of 5 + 6 into an HTML paragraph element using innerHTML, into the HTML output using document.write(), into an alert box using window.alert(), and into the browser console using console.log() for debugging purposes. The document explains different methods for displaying data in JavaScript.