What language(s) do I need to know to develop plugins/extensions for Firefox? Also, any useful tools (as far as IDE or SDKs)?
Plugins and extensions are two very different things. Plugins are like Java, Adobe Reader, etc. Extensions are the more common of the two and typically what you find on addons.mozilla.org.
mozdev.org has some good resources for creating extensions. You don't really need an IDE or SDK's as it is primarily JavaScript unless you want to implement something like XPCOM.
developer.mozilla.org is also a good resource.
Firefox uses XUL, a anguage similar to HTML. If you know HTML, XUL will be easy to learn. In fact, Firefox is completely made in XUL.
Take a look at this link inside Firefox: chrome://browser/content/browser.xul
And basically an add-on is like a much more powerful web page (actually you can make an application based in XUL just like Firefox is... and use XULRunner to run it on any OS (and even from the web!), with all of Gecko's rendering power for free).
Links:
You would want to have an idea of how markup
languages work. The development of extensions or add-ons is done in XUL
and XPCOM
(I am assuming you did not mean plugins, pardon me I am wrong and this answer then would be only half of what you want to know.)
This is a handy guide to developing add-ons from Mozilla's website.
HTML, XUL, Javascript, C (if you're forced to use XPCOM).
Pick your favorite editor.