Are you 100% dedicated to C++? If not, I would recommend starting with XNA/C# instead. DirectX will force you to spend a lot of time up front learning API calls before you ever get something on the screen. XNA will allow you to start coding your game very quickly while getting immediate feedback while you program.
If you are committed to C++, I would recommend Beginning Game Programming by Jonathan Harbour. He starts with an easy to understand framework that won't take long to pick up. Remember that to use DirectX you will have to learn win32, and low level DirectX code.
For tutorials, try googling "c++ beginning game programming tutorial". Gamedev.net will be another invaluable resource. Go to the "For Beginners" forum and look through the stickies.
As for what you must know, it depends on your aspirations and your choice of tools. As a beginner, you will want to start small and in 2D or text games. To get a Pong game going in XNA, you only need to have basic C# skills and basic collision detection. To get a Pong game going in DirectX, you will need to understand win32 code, and a ton of device calls. To do a console text game, you only need to know basic C++ and maybe some basic gameflow techniques.