Installing software on linux is different than windows.
There are several types of files that can be installed. For a distro like Fedora, the best and easy way is to set up online repositories, download .rpm files, and use rpm to install them. That will take care of all pre-reqs. Firefox may be on their repos, you would have to look.
You can also get programs like Firefox from Mozilla. Firefox from mozilla is compiled into binary files. Once downloaded, you will find the instructions to install it on Mozillas web site.
You said it was a .zip file? Are you sure you downloaded the linux version? zip files are usually for windblows. This link --> http://www.mozilla.com/en-US/firefox/all.html
has versions for winders, macs and linux. Get the linux version.
It should be a .tar.bz2 file.
This link --> http://support.mozilla.com/en-US/kb/...refox+on+Linux
shows you how to install it.