The Modern UI version of Firefox for Windows 8 has been ripening for a while. Development began last March, and experimental builds appeared in the "Elm" development branch in October. Since yesterday, though, you can grab Firefox with a side of Modern UI right from the main nightly channel.
Here's what Firefox Desktop Product Manager Asa Dotzler wrote about the release on his blog:
On Tuesday, our preliminary Metro Firefox development work arrived at mozilla-central, the source code repository that feeds the Firefox Nightly channel. This means that if you are on the Firefox Nightly channel and you have a Windows 8 device, your Wednesday Firefox update should deliver a Metro Firefox tile to the far right end of your Windows Start screen.
There's plenty of work still to do, but it's stable enough that we're ready for more and more regular testing. If you're a Firefox or Windows developer and you'd like to get involved, please let me know.
Trying the Modern UI-infused nightly is pretty simple. Head to the Firefox Nightly page, grab the standard Windows installer, and let it do its thing. When you're prompted to make Firefox Nightly your default browser, say yes. A blue "Nightly" tile will then appear on your Windows 8 Start screen. (Yes, you do have to make it your default browser; otherwise, a different Modern UI tile will show up, and that one will simply open the desktop version of Firefox.)
As far as I can tell after a quick look around, Firefox for Modern UI works quite nicely. It's fast and elegant, and it syncs bookmarks with its desktop counterpart, just as one would expect. The interface isn't a very big departure from Internet Explorer's, but I suppose that's not a bad thing—swiping down to access tabs is convenient enough, and it avoids cluttering up the screen like Chrome does.