Windows

1. Download a static build of ffmpeg from here.
2. Use your favorite file archiver to unpack it in the folder of your choice.
3. Add the bin folder to your path. Using cmd.exe with admin rights: setx /M PATH "path\to\ffmpeg\bin;%PATH%"

Linux

On most Linux distributions you can just use your default package manager.

Ubuntu

# apt install ffmpeg

Arch Linux

# pacman -S ffmpeg