The solution depends on the actual problem: why exactly can't you play songs? Because there is no codec so your player application doesn't know how to play the audio, or because you get no sound though the song seems to be playing, or because your player tells you there is a problem with your soundcard, or something else maybe?
Before going further, I'll just mention that though some people surely love RealPlayer, I wouldn't recommend using it unless it's really the only choice, and that's very rarely the case. The usual player engines (Xine, GStreamer, ...) and apps like MPlayer or VLC player ought to be able to play most of the formats you play.
If it's about codecs - you have audio in digital format, say a .mp3 file for example, and you can't play it (player says "unrecognized format" or something), the solution is to install the required codecs or libraries for your audio player engine (backend, call it what you like) so that it is able to decode and thus play the format. First of all you should know whether you're using GStreamer, Xine or something else - that is, if you are using player apps like Rhythmbox or Totem. If you find out you're using GStreamer, pop up your RedHat's package manager and select to install gstreamer-plugins packages (gstreamer-plugins-good, -bad, -ugly, what ever there are). If you find out you're using Xine, use the package manager to install Xine's extra libraries/codecs (the naming might vary, but something like libxine-extracodecs or xine-libs-extras or such). Or if you're using MPlayer as your player, make sure you have installed the w32codecs (mplayer-codecs?) (available at mplayer's site if nowhere else).
If it sounds difficult, don't worry - the web is full of howtos about this thing. Very probably if you find a Fedora-related howto, it works for you too, if you can't find RHEL specific help.
In the end it's just about locating and installing one or a couple of rpm packages; preferrably trough the graphical package managing application, because that is the easiest way.