Read google voice search mozilla firefox for more information.
You can use google voice search on Mozilla Firefox using a Mozilla extension called Voice fill.
You can download the extension from here.
Voice Fill uses speech recognition to enable voice search on Google, Yahoo and Duck Duck Go search pages. You can see it in action in this video:
Voice Fill is multilingual.
To change it to match your own language, navigate to about:addons, then click the Preferences button next to the Voice Fill icon. There you can also choose your preferred search engine in order to have it opened by default when you click the microphone icon in your toolbar.