First, I should be clear that this was done on a G2 AWS instance and I started with working nvidia support by following http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/using_cluster_computing.html
From that (or if you're feeling more bold), the thing to take is getting the right binary install package and running it. Look at http://www.nvidia.com/object/unix.html and get the package you want (at the time, I'm using 'Latest Long Lived Branch version: 361.45.11'), then run the file you get. For example,
sudo sh ./NVIDIA-Linux-x86_64-361.45.11.run.
I do not have time to test on a clean instance so you may need a bit more setup that I've not mentioned and I make no guarantees anyway since I hardly know what I'm doing here :)
The ffmpeg_build.sh script was mostly copy/paste from the guide at https://trac.ffmpeg.org/wiki/CompilationGuide/Centos and with significant help from folks on FreeNode #ffmpeg (notably furq and JEEB though there were others).
The steps for adding OpenCL headers support was borrowed