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. We'll use the MinGW-w64 toolchain to accomplish this.
Note: MinGW-w64 is a fork of its predecessor, MinGW. They are different. If you install MinGW-w64 in a different way than shown in this document, make sure you have MinGW-w64, not just MinGW!