Neothyne only depends on SDL2. Make sure you have it installed correctly for your tool chain and Neothyne should build out of the box.
Linux users can build Neothyne from source by invoking make.
$ make
BSD users can build Neothyne from source by invoking gmake.
$ gmake
Windows users have a couple methods for building Neothyne.
The preferred method for binaries is to use the included Visual Studio solution with Visual Studio 2015 or higher.
In Visual Studio launch the NuGet package manager and run
PM> Install-Package sdl2
Visual Studio 2015 project files are setup to produce binaries using a relatively new C run time. If you need binaries on older versions of Windows, change the runtime library or use the alternative method.
The alternative method is to use a MingW toolchain with a version of gcc >= 4.9.2 Optionally you can use a version of clang >= 3.6.0 in place of gcc
$ make -f Makefile.mingw
The compiler can be set with CC=clang if you prefer to use clang.
$ make -f Makefile.mingw CC=clang
You can optionally build Windows binaries on Linux using a cross compiler using this Makefile