It really depends on what you downloaded, you didn't shared anything about the firefox archive that you've downlaoded, but there can be only two cases,
1. You downloaded the source code.
In this case, you'll need to make, compile, install, run the installer etc.
2. You downloaded the portable version.
If this be the case, you can run it directly as instructed here.
- Download Firefox from the Firefox download page to your home directory.
- Open a Terminal and go to your home directory: cd ~
- Extract the contents of the downloaded file: tar xjf firefox-*.tar.bz2
- Close Firefox if it's open.
- To start Firefox, run the firefox script in the firefox folder: ~/firefox/firefox
Firefox should now start. You can then create an icon on your desktop to run this command.