You can try yum from the command line or eventually rpm (both as root). The former will try to resolve dependencies for you, the latter will simply complain if some dependency is not met. So, do either
yum localinstall skype-blah-blah-blah.rpm
this will ask for confirmation before installing, or
rpm --test -Uvh skype-blah-blah-blah.rpm
this will simply test the installation (option --test) and will tell you about additional required packages. I suggest to try the first one, using yum.
Edit: another option is to right-click on the rpm icon and chose "Open with Software Manager" or something similar. On F10 it should launch the PackageKit installer.