I also wanted to say that wile you are searching for state machine examples you should note that most of them are only showing the simplest state machine examples with very low complexity like general game state (whether you are in main menu, is game loading or is the game in progress for instance).
But the state machine that you will need for your game will probably need to have much higher complexity. But don't let that discourage you.
Also you might want to check Decision_tree and Behavior_tree concepts.
Now while these two concepts are most often used for implementing AI they can also be used for controlling your game state.