Check out the source code from the git repo.
Open the solution (.sln file) for your platform (Linux, Windows/RT, OSX) using either MonoDevelop/Xamarin Studio (Linux and OSX, respectively) or Visual Studio 2013 (C# Express).
Compile the code.
Before running the game you must copy over the data files from a Warcraft 1 retail or demoe version. To do that, copy everything from the DATA directory of Warcraft 1 (contains 40 .WAR files in retail, but only one .WAR file in the demo version) to a subdirectory named "Data" below the "Assets" directory in the output folder containing the binary (usually bin/Debug, but that differs depending on platform).
Run the WinWarCS executable either from your IDE or from disk.
Enjoy