1. Switch to root

    su
    
  2. 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
    
  3. Update all yum packages

    yum update
    
  4. Install the Flash Plugin

    yum install flash-plugin
    
  5. Restart Firefox or your default browser and the Flash Player should now work on Fedora Core 15 32bit