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Yes, Firefox 3.0, 3.5, and 3.6 will work on Windows 7 just the same as they did on previous versions of Windows. When the Firefox window is open and visible in the bottom taskbar, there will not be any added options like some other Windows 7 applications.
For instructions on how to install Firefox, see How to download and install Firefox on Windows.
Firefox is currently a 32-bit application, but will work on 64-bit versions of Windows 7. Mozilla is working on a 64-bit version of Firefox for Windows, but this version has not yet been scheduled for release.