Click on the down-arrow next to the yellow helmet icon in the addon bar (top-right of the window) to change the User Agent for the current domain. Notes: the add-on bar may not be displayed by default. In this case, right click on the Firefox menu and select «Add-on bar». If you install it on Firefox 29, the icon will not appear by default, you will have to manually add it (I may fix it if I have some time).
Click on the helmet icon to quickly enable/disable this add-on.
If the page performs requests on other domains, the default UA will be used until a UA is explicitly specified for each domain.
Restarting the browser is not required.
Remember that any request will pass though the extension, which should slow down a little bit the browsing. In the configuration window, you can disable the replacement so you use it only when you really need it.
Warning: in several cases (including when Firefox crashes), your settings may be lost (because of a Firefox bug). I will work on a work-around when I have time.
A complete list of UA is available on this page.
Known issues and possible improvements: