In the game hacking community "injecting" refers to the process of attaching code into the process of a program. A good example is code responsible for keeping your health at a static value (i.e. god mode).
There are a few code injection tutorials around that teaches you some methods, although writing undetectable code injectors is a lot more complicated for beginners. Most anticheating systems have to do with online games. You could actually get into trouble using/writing hacks for online games because it ruins business.
For a beginner looking how to inject code, there are a few tutorials around that could assist you.
Usually when you see D3D hacks, it is referring to modifying the routines done with DirectX, which is a graphics API that most video games use. This makes it possible to create hacks like chams/wallhacks.
My advice to a beginner would be to start off with single player video game hacks first. Once you're familiar with hacking without worrying about working around anti-cheat detection, you can start learning how to circumvent that. However, as I said before although online game hacking is pretty widespread, it can affect business and you run the risk of getting a lawsuit filed against you. Most people think it isn't wrong because hacking is done through their own code, but that's not the issue at hand. Think of it this way, is it legal to hack a bank system to wire money into your account? When money is involved in a game and you hack to gain an advantage that links to that, things start to get sketchy.