the inner voice
Those who believe in the existence of a higher power often pray during times of trouble or duress. Since Shenaniganists don't have a deity, they don't pray. But they do believe that each person innately knows the right action called for in most situations and may engage in meditation or quiet contemplation in order to better listen to this inner-voice.
Say a Shenaniganist is out enjoying a lovely dinner with her family when she looks up and sees her friend's fiancée across the room canoodling with another woman. The Shenaniganist is torn, should she tell her friend what she has seen? A religious person might feel this is a time to pray and ask their god for the answer, while a Shenaniganist turns to her inner-voice for guidance.
She inherently knows that what she has seen is wrong and that her friend should be made aware of the situation, but she also knows how much finding out will hurt the friend. She is concerned, too, that if she goes to her with the truth, her friend may resent her for butting in. On the other hand, if she remains silent and the fiancée continues to cheat, the friend may later find out that she was aware of it and be angry that she wasn't told.
Through introspection and paying attention to her internal voice, she becomes aware that her dilemma is not whether telling her friend is the right thing to do, it's her fear of how bringing the situation to her friend's attention will affect her. She realizes that what she wants is a guarantee – to be able to tell the truth and have her friend be grateful and thank her for it. But Shenaniganists know there are no guarantees for doing the right things beyond the satisfaction of doing them.
The more a Shenaniganist practices listening to that voice, the more self-knowledge she gains and the more comfortable she becomes with the decisions she makes. There will still be times when choices are difficult, but Shenaniganists take comfort in knowing that they are their own choices, based in personal responsibility and the instinctual knowledge of right and wrong.