The following steps describe how to build FFMPEG on the Debian system from source. The Debian Jessie is my current server version. The FFMPEG steps pipeline is: Get and install prerequisites, download FFmpeg, unpack FFmpeg source, configure installation and build the solution. Easy and straightforward as possible. 

Debian installation steps for FFMPEG

You need to install some prerequisites.
sudo apt-get -y install git make nasm pkg-config libx264-dev libxext-dev libxfixes-
dev zlib1g-dev
Download FFMPEG from the website
sudo wget -O ffmpeg-2.8.tar.bz2 "https://www.ffmpeg.org/releases/ffmpeg-2.8.tar.bz2"
Unzip and remove original package if you like

sudo tar -xvf ffmpeg-2.8.tar.bz2
sudo rm -Rf ffmpeg-2.8.tar.bz2 

Run configuretion in source Folder 

./configure --enable-nonfree --enable-gpl --enable-libx264 --enable-x11grab --enable
-zlib

Build solution
make -j2
Note here. -J 2 depends on your number of processor cores. If you have 20 cores intel machine. Lets Run make -j 20

Install and configure FFMPEG
sudo make install 
sudo ldconfig -v