I have some ideas for some games, but they are too advanced for me to create at this point.
Still, I want to create the engine myself, for the knowledge.
Where can I possibly learn this?
I have also heard that to make games with C++ you need DirectX or OpenGL.
What are these, and why do you need them with C++, and not Java?
Also, thank you for the links! I will read them!
Actually, depending on what kind of game you are making, you won't necessarily need either Direct X or Open GL. Have a look at NetHack, for instance. That is a full game where all you need is the console. Also, if you are making a Othello, Chess, Mine Sweeper kind of game, you can just use a normal canvas type of GUI object for your operating system.
Of course, Direct X and Open GL are graphics libraries that are closer to the hardware itself, and are much faster than any canvas any GUI component can give you, at least it were so in the past. It is also specialised in processing graphical data, wether it is 3D or 2D, so it beats anything you would do in pure software. Nowadays you can even offload computations formerly done on the CPU to the processor on the graphics card. It is also much more complex (but not necessarily so much more complex than to write graphics application in pure software, which is slow), so it really depends on which aspect of game creation you are looking into at the moment. You don't explicitly need C or C++ to use Open GL, I believe you can nicely make Open GL applications in Java. Here is one project aimed to enable that, that I know nothing about: http://jogamp.org/jogl/www/
If you start small, you will slowly master the art of making games. It is much more fun to make a Mine Sweeper clone than you think. There are some hidden things that are not apparent right from the start, for instance, what if you click a large area that has no surrounding mines? There you would stumble across making a recursive search to find all the adjacent safe slots on the map. Recursion is not really hard once you have learnt it, but it may be hard entry point, just like the concept of pointers, for instance (which Java doesn't have, just references).
Good luck! You are into a lot of fun learning.