Follow these steps
Install skype requirements - part 1
sudo dnf install alsa-lib.i686 fontconfig.i686 freetype.i686 glib2.i686 libSM.i686 libXScrnSaver.i686 libXi.i686 libXrandr.i686 libXrender.i686 libXv.i686 libstdc++.i686 pulseaudio-libs.i686 qt.i686 qt-x11.i686 zlib.i686 qtwebkit.i686
Install skype requirements - part 2
sudo dnf install alsa-lib.i686 fontconfig.i686 freetype.i686 \ glib2.i686 libSM.i686 libXScrnSaver.i686 libXi.i686 \ libXrandr.i686 libXrender.i686 libXv.i686 libstdc++.i686 \ pulseaudio-libs.i686 qt.i686 qt-x11.i686 zlib.i686 qtwebkit.i686
Download skype to the /tmp folder
cd /tmp
wget --trust-server-names http://www.skype.com/go/getskype-linux-dynamic sudo mkdir /opt/skype sudo tar xvf skype-4.3* -C /opt/skype --strip-components=1
Create the symbolink lynks to skype
sudo ln -s /opt/skype/skype.desktop /usr/share/applications/skype.desktop
sudo ln -s /opt/skype/icons/SkypeBlue_48x48.png /usr/share/icons/skype.png
sudo ln -s /opt/skype/icons/SkypeBlue_48x48.png /usr/share/pixmaps/skype.png
4.Create the skype shell file
sudo touch /usr/bin/skype
sudo chmod 755 /usr/bin/skype
cat << EOF > /usr/bin/skype
#!/bin/sh export SKYPE_HOME="/opt/skype"
\$SKYPE_HOME/skype --resources=\$SKYPE_HOME \$*
EOF
5.Finally execute skype