Posted on To update to GNOME 3.16 with Fedora, it is first necessary to update to Fedora 22 from Fedora 21. To do this, first open a terminal and as root (i.e. sudo) and run the following commands:

sudo yum install fedora-upgrade 
sudo fedora-upgrade

This will update to the next highest upgrade available. In this case it will update Fedora 20 to Fedora 21. Next run

sudo rpm --import https://getfedora.org/static/8E1431D5.txt
sudo yum update yum
sudo yum clean all
sudo yum groupupdate 'Minimal Install'
sudo yum --releasever=22 distro-sync --nogpgcheck

If there are any problems running sudo yum --releasever=22 distro-sync --nogpgcheck, try the following instead:

sudo yum --releasever=22 distro-sync --nogpgcheck --skip-broken

If the problem persists you may wish to manually install the program causing trouble. But if so, do this with extreme caution by checking the program you are removing is not a core part of your install!

To install the GNOME Desktop simply type the following into the terminal:

sudo yum groupupdate "GNOME Desktop"

Parts of this instruction were borrowed from The Fedora Project Wiki