And if you use yum, you (almost) never need to worry about the architecture.
If you manually download an rpm for something not in the Fedora repositories, then first type
in a terminal. Most likely it will give you "x86_64" or "i686". You then need to have rpm files that match that architecture; note that all of i386, i486, i586 and i686 can be installed on an i686 system, but x86_64 can't. Also, some rpms have "noarch" in the name, which is short for "no architecture" and really means "suitable for any architecture".