Pterosaur gives you all the power of real Vim in all Firefox textboxes. Unlike similar extensions, it does not approximate or emulate Vim or open a Vim instance in a new window.
Pterosaur uses an actual Vim instance to process text entered into textareas, inputs, Codemirror, Ace, contentEditable, and optionally, chrome areas like Firebug and Developer Tools. Pterosaur, itself, is only used for text editing, but supports optional integration with Pentadactyl or Vimperator.
See http://github.com/ardagnir/pterosaur for more frequent updates and more detailed instructions and documentation.
To see Pterosaur in action, watch:
Pterosaur v1.0 demo
Pterosaur v0.8 demo (with Pentadactyl integration)
Note that since Pterosaur sends many of your keystrokes to vim, and may temporarily store text on your hard drive, you should be careful about using it for sensitive data. Pterosaur is disabled by default for password fields and private browsing windows.