I bought a book called something like Android 4 Games Programming (can't remember the exact title). It was really good. You start with super basic xml games and finish with more complicated directX games. Books like these go through every single step from vector calculations into game logic. Youtube and other online tutorials can be quite "cheesy" in the sense that they talk a lot about something, but leave very essential items out. Books are good since there are versions of them and they are thoroughly reviewed before let out on the market. So save yourself some time (=money) and go buy one of these books. There is probably one for each language/platform at Amazon. I chose Android since it's based on Java (popular language) and all the development tools are free. If you choose something like C# or any Apple languages you might have to pay some for the development tools.
- You don't have to pick Android programming - but buy a good book!