The best way to install software is to find precompiled packages for Fedora Core 2, for the application that you want. Precompiled packages are .rpm files. Packages compiled specifically for Fedora Core 2 usually have "fc2" in their name.
You can use this link for the official packages :
http://www.fedoratracker.org/tracker.py?mode=pkgSearch
Otherwise you can query Google. For Mozilla Firefox you would query "Firefox fc2 rpm". You will get a hit from Dag Wieers repository (a well known packager for Fedora).
http://dag.wieers.com/packages/firefox/
Download firefox-0.9.2-3.1.fc2.test.i386.rpm
To install it, open a command prompt window (Explore->Accessories->Command Prompt). Switch to root by typing "su" and your root password (the one that you gave during the installation). Go to the directory where firefox-0.9.2-3.1.fc2.test.i386.rpm is saved using the "cd" command. Type rpm -i firefox-0.9.2-3.1.fc2.test.i386.rpm
That's it!
I hope this helps!