Vulkan-Tutorial.com, while not affiliated with The Khronos Group, is a good read to understand how the Vulkan API is structured. It is set up like the tutorials I followed when learning WebGL, which seems to make it quite approachable. I mean, we are still talking about the Vulkan API, which was in no way designed to be easy or simple, but introduction-level material is still good for developers of all skill level, unless they're looking for specific advice.
To emphasize what I mean by “approachable”, the tutorial even includes screenshots of Visual Studio 2015 at some points, to help Windows users set up their build environment. Like… step-by-step screenshots. This explanation is also accompanied by Linux instructions, although those use Ubuntu terminal commands.