Modern Web browsers are designed to provide the fastest browsing experience possible for users. They use technologies such as caching (saving parts of the page locally for future visits) that are great for end users, but can be major annoyances when developing websites. To switch these features off selectively, I use Web Developer for Firefox.
Compared to Mozilla's carefully structured Firefox add-on Firebug, Web Developer feels more like a random collection of tools. Random does not mean haphazard, though: Each of the tools has its use, and they can all come in handy at one time or another. Two quick examples: the Display Image File Sizes option in the Images menu lets you audit an entire page for large images at a glance, and the Outline Tables option in the Outline menu lets you quickly see if tables were used properly (to display tabular data) or as crutches for page layout instead of DIV elements (like in 1998).
Because Web Developer is not thoroughly documented and is built as a toolbox of loosely-related utilities, the best way to become familiar with it is just to play around with it. Thanks to its simple layout, you can simply browse through the menus once and figure out what most items do based just on their labels. If you get stuck, you can always check the brief FAQ posted by author Chris Pederick. It is not extensive, but might help you out of a bind.