You don't. It's sad to say, but AMD's proprietary drivers do not work on kernels 3.19 or newer. Bug reports filed. All we can do is wait for a new release.
you could give it a shot and try this: Installing the Proprietary AMD Catalyst 15.5 (fglrx 15.101) driver on Fedora 22 with Linux Kernel 4....
At least it made me 15.101.1001-150414a-184705C work with 3.19.8-100.fc20.x86_64
What flavor are you using? Will make a difference between the solution. And also, if you have a Fury X, it's still unsupported in 4.1 kernel. (Patches have started making their way in but largely suspected to hit mainstream in 4.3 kernels.)