A Firebug developer utilizes the Firebug web development tool to debug, edit, and monitor CSS, HTML, and JavaScript live on any webpage. They can inspect elements to understand the association between the HTML elements and the styles applied to them. They analyze network activity to identify bottlenecks and optimize performance. They debug and profile JavaScript by stepping through the code to pinpoint the root of a problem. They also monitor and manipulate the Document Object Model (DOM) in real-time. Furthermore, they tackle layout issues using the layout and box model representation. They essentially enhance web application functionality and troubleshoot issues.