What I'm trying to do is to save the changes I make to CSS and HTML on different sites with Firebug.
Just to be clear, I don't expect Firebug to upload the changes to the server via FTP or anything. I just want to save the changes locally, so only I will be able to see them.
For example I've seen a few Firefox/Chrome extensions that add a download button under every video on Youtube, so I know it's possible to do that somehow.
If you have a different way to achieve what I'm trying to do, I'll be glad to hear about it.
(It doesn't have to be with Firebug.)
Thanks in advance!
You could try using Greasemonkey.
It has support for adding custom scripts that are run whenever you load a page (linked to which pages it should load on) and that can make changes to the page dynamically.
https://addons.mozilla.org/en-US/firefox/addon/greasemonkey/