Switch to root
su
Add the neccesary software sources to the yum repository
rpm -ivh http://linuxdownload.adobe.com/adobe-release/adobe-release-i386-1.0-1.noarch.rpm rpm --import /etc/pki/rpm-gpg/RPM-GPG-KEY-adobe-linux
Update all yum packages
yum update
Install the Flash Plugin
yum install flash-plugin
Restart Firefox or your default browser and the Flash Player should now work on Fedora Core 15 32bit