Update doesn't work in yum when the system can't find an update in the repositories. Most of the distros have a delay between the release of new packages their appearance in repositories. I just had about three days on Fedora Core 8/9 last week (before deciding it wasn't what I wanted). I got it working well enough to try it out by adding freshrpms to my list.
Generally, you can search out a repository which has what you want on-line, then follow instructions such as these:
http://www.gagme.com/greg/linux/f9-tips.php#repos
They presuppose, of course, that you are running a recent version of Fedora or of RHEL. That's something you haven't said, and it makes a difference. I last spent serious time on Fedora/Red Hat when yum was just being introduced, and I became quite familiar with rpm's capabilitles in those days. If you have internet access and know the address of a package, you can have rpm download it for you. There are other ways to do it, though. Including manually edit the yum configuration files. I did that during another short stint with Fedora. Don't. Do not.
If you're version of Red Hat is more than a year old, it is a very good idea to upgrade. Again, information on doing that is all over the web, It's on the page I cited above.
There is a third possibility for updating firefox, which is what you wanted: use the Mozilla release. Generally I recommend against it, and having started to use it on Red Hat Linux before Red Hat/Fedora Linux supported it, I recommend against it. The tweaked version is stable in a way the Vanilla version is not. (the tweaked version being the one available on RPMS
EDIT: Now that you have told us which version of Red Hat you are using here is some more specific information:
http://www.linux.com/feature/118304
Use this link to get the package and install it. Get it then install it using RPM.
http://download.fedora.redhat.com/pub/epel/4/i386/repoview/epel-release.html
Here is another piece on adding third party repositories:
http://www.beginlinux.com/desktop_training/newbie/repos
Once you've done that, if you can't install the Firefox package, you should be able to find and install the missing repositories.
I do recommend upgrading if you're using Red Hat, though.