My advice for you is to actually just learn to program in a specific language, be it C++ or C# or Java ... whatever you choose and whatever feels like you would love programming in. Solve problems in that language and do a lot of exercises to improve your logic. Write code everyday and tackle as many problems as you can find and you can find a lot of them. There are sites that offer them, there are books that train you to think in a certain language and so on. Game developing, in my opinion, is rarely useful. I used to play video games, I don't any more. They are a waste of time and resources. It's much better to go outside and play tennis, football, handball ... whatever you like. But if you learn Math, Physics and a programming language very well, you can do useful stuff with them.
Programming is NOT like Olympic gymnastics or concert violinist. You don't have to start young.
I took my first programming course when I was 20. I took 4 programming courses in college and was hired as an entry-level programmer after I graduated at 22.
Try Python
http://www.greenteapress.com/thinkpython...
http://docs.python.org/2/tutorial/index....
http://www.tutorialspoint.com/python/
http://learnpythonthehardway.org/book/
Because you are young, it isn't surprising that you are focusing on games, however, most programmers work on business programs.
Im 16 and at school ive chosen computer science , maths, physics and art . My goal is to be a computer game programmer/( maybe designer ). I dont know if its too late or not to start because i read people starting at when they where 13 and stuff... Even though im going to start learning at school i would like to learn at home aswel more. So i would like to know of any good sites that teach you or any advice on this subject and how to self learn.