I'll explain how to create programs that run on Windows (.exe files) from a Linux machine. I'll explain how to compile C and C++, and how to make 32- and 64-bit programs. I'll also explain how to use third-party libraries (we'll use SDL2 here), and how to distribute the programs.
To cross-compile for another architecture, you first need to know what architecture you're compiling for. The important part here is the target triplet. It's typically in this format: