DOM Inspector is a tool that can be used to inspect and edit the live DOM of any web document or XUL application. The DOM hierarchy can be navigated using a two-paned window that allows for a variety of different views on the document and all nodes within. This screenshot shows a typical inspecting session.
You will find it under the Tools > Web Development menu in any Mozilla window.
Run: /path/to/mozilla -inspector [url]
First you must install the sidebar, via Edit > Preferences > Advanced > DOM Inspector. After you have done that, simply open up the inspector panel and visit a website. It's that simple!
Start playing with it and you'll get the hang of it. Formal documentation is still under development, but there is a short FAQ available.
Use the conveniently named "DOM Inspector" component in Bugzilla. If you have any questions or ideas for improvement, visit caillon in #inspector on irc.mozilla.org.