The primer is simple: if you notice that your code is using too many if statements, especially nested ones, and you are starting to wonder if you are covering all alternatives and cases, then using the rigor of a state machine may help.

You know, that kind of code:

  if(start) {
    if(!running) ...
  }
  
  if(stopped & !jumping) {
  } else if(running) ...

Stop and write a proper case statement (aka a state machine). You may discover that combinations of booleans (in my example, stopped & !jumping) deserve to be their own state. The insight is that the resulting code should be one clean case statement, with no nested ifs allowed. Then you know you cover all the states/cases.