We have had this question several times, so here goes (all commands are in bold, and should be executed in a terminal as root unless otherwise noted):

1. If your distro provides FireFox as an installable package, I would install it that way. Gentoo and Debian{SID and Sarge, not Woody} do provide this as a package directly. It is avialable for Fedora and RedHat 9 via apt. If you need to install the version from the Mozilla Site, do so as follows.

2. Go to the FireFox site and download the gtk2+xft version of FireFox for linux. (It is currently a link in the top left hand corner of their page). Currently (at the time of this guide being written) the file name is firefox-0.8-i686-linux-gtk2+xft.tar.gz.

3. Open a terminal, switch users to root (if you are not already logged in as root) with this command:

su - root

4. Change directories to the place where you downloaded the file to. Untar the file with the command:

tar -xvzf firefox-0.8-i686-linux-gtk2+xft.tar.gz

5. That should create a directory called firefox, that contains the firefox program files. Move the firefox directory to /usr/lib with this command:

mv firefox /usr/lib

6. Verify that firefox directory is indeed moved to /usr/lib with this command:

ls -al /usr/lib | grep firefox

the result should look similar to this:
CODE
drwxrwxr-x    9 64245    11407        4096 Apr 23 18:31 firefox


7. Create a link in /usr/bin that points to the executable file called firefox in /usr/lib/firefox like this:

cd /usr/bin
ln -s /usr/lib/firefox/firefox .


8. Now verify that the link is correct with the command:

ls -al /usr/bin | grep firefox

The result should look similar to this:
CODE
lrwxrwxrwx    1 root     root           24 Apr 16 06:09 firefox -> /usr/lib/firefox/firefox


9. Create a launcher (ie shortcut) on your desktop or in your menu to launch /usr/bin/firefox...or you can launch firefox from a termial with the command:

firefox

10. See this link for how to setup firefox to open up your e-mailer for mailto links and this one to make it your default browser in gnome.