This is a short guide on how to install MinGW and MSYS using the latest stable.
Download the MinGW installer from www.mingw.org/wiki/HOWTO_Install_the_MinGW_GCC_Compiler_Suite. (As of this writing, the download link is a bit difficult to find; it’s under “About” in the menu on the left-hand side). You want the file entitled “Automated MinGW Installer” (currently version 5.1.4).
Run it and install MinGW. Only the basic package is strictly needed for Cython, although you might want to grab at least the C++ compiler as well.
You need to set up Windows’ “PATH” environment variable so that includes e.g. “c:mingwbin” (if you installed MinGW to “c:mingw”). The following web-page describes the procedure in Windows XP (the Vista procedure is similar): support.microsoft.com/kb/310519