How do I open a Windows NT OpenGL window?

Efficient vendor-supplied implementations of OpenGL (making use of graphics acceleration hardware to a greater or lesser extent) exist for Mac OS, Windows, Linux, many Unix platforms, Wii and PlayStation 3. Various software implementations exist, bringing OpenGL to a variety of platforms that do not have vendor support. Notably, the open source library Mesa is a fully software-based graphics API which is code-compatible with OpenGL. However to avoid licensing costs associated with formally calling itself an OpenGL implementation, it claims merely to be a "very similar" API.