compiling extensions on Windows 64-bit and Python 3.5

How to compile on Windows 64-bit (for example with Anaconda)? It seems things got complicated when developing on/for Windows: you need to use the same compiler version as the one that was used for Python and all its extensions. We need to figure out and document how to setup a Windows build environment for Python extensions!

Some more background information:

• Using Microsoft Visual C with Python
• Compiling C extension modules on Windows. The Cython wiki re-iterates what is said elsewhere: MinGW 64-bit is not in a usable or stable state. Otherwise 32-bit is ok (if your Python version is also compiled with that)
• Building extensions for Python 3.5 (on Windows)