Recommended compiler: the latest build of mingw-w64 from Mingw-builds
Download SDL and its relevant extensions: You will also need libogg, libvorbis, libvorbisfile. If building them from source is inconvenient, you can download them built for Windows (Courtesy of Brent Bessemer) from here.
Linux (Debian)
Grab the necessary development libraries on Linux with Debian, using this command:
sudo apt-get install libsdl2-dev libsdl2-image-dev libsdl2-ttf-dev libogg-dev libvorbis-dev
These are the names in the Ubuntu repositories, for other distributions they may be different.