I was trying to install Java on CenOS but had a very hard time doing so. I found many tutorials but none worked. Most tutorials did not say you need to download compat-libstdc++-296 compat-libstdc++-33 so that made it more frustrating. This worked for me. I make no guarantee it will work for you. Be sure to switch to root for this to work and download to your /tmp folder.

Download jre-6u17-linux-i586-rpm.bin ( http://www.java.com/ )
su
yum install compat-libstdc++-296 compat-libstdc++-33
cd /bin
sh /tmp/jre-6u17-linux-i586-rpm.bin
cd /usr/lib/mozilla/plugins
ln -s /usr/java/jre1.6.0_17/plugin/i386/ns7/libjavaplugin_oji.so .

Close and reopen Firefox.