First download the Sun/Oracle JRE from their web site in RPM format. The JRE in Fedora does not work. You have to get the one from Sun.
yum install ./jre-7u55-linux-x64.rpm
Create a directory for it:
mkdir -p /opt/minecraft/client/
Download the software from here:
cd /opt/minecraft/client/ wget https://s3.amazonaws.com/MinecraftDownload/launcher/minecraft.jar
Download the icon:
wget -O icon.png http://www.minecraftwiki.net/images/c/c5/Grass.png
Create a desktop icon to run it. Do this as the user you want to see the icon.
cd ~/.local/share/applications vi minecraft.desktop
Now put the following in the minecraft.desktop file:
#!/usr/bin/env xdg-open [Desktop Entry] Name=Minecraft GenericName=Minecraft Comment=Sandbox mining game Exec=/usr/java/jre1.7.0_55/bin/java -Xmx1024M -Xms512M -cp /opt/minecraft/client/minecraft.jar net.minecraft.bootstrap.Bootstrap Icon=/opt/minecraft/client/icon.png Terminal=false Categories=Application;Game Type=Application
It should now show in your installed Applications under Games.