I'm trying to install caffeine on Fedora but I am stuck on some problem, that is I can't run:
Fedora is RPM based, so to install, in a konsole, type as root: 'rpm -ivh caffeine*.rpm' (if you already have the package downloaded) or type 'urpmi caffeine' and the package will be downloaded and installed automagically.
FYI - the link you provided is to an Ubuntu Linux managed site working with Ubuntu based packages. Assuming that this package has been built for Fedora, then the steps I've outlined will work. If the package has not been ported to Fedora and placed out in their repositories, then those commands will fail. In that case, then you will have to download the source tarball and build the package yourself.