Exploring the features of Firebug, with code examples covering using the console, timing code, stack traces, debugging and breakpoints, profiling, tracing HTTP requests. An excellent overview of Firebug's functionality
Joe Hewitt, in this Dr Dobbs article talks about using the Firebug extensions to inspect and debug Ajax applications (or any browser-based JavaScript application). It also has CSS inspecting capabilities, editing JavaScript on the fly, inspecting HTTP request and responses, logging, breakpoint debugging and profiling. A useful howto.
Apart from being an elegant debugger, FireBug offers the developer hooks that can be used from JavaScript, offering logging, assertions, performance measuring, and command line functions for inspection or traversing a document.