The strategy I would use to find symbols in stories is first to read the story two or three times, and the second time start making notes of things that are repeated more than usual, things that stand out or are very unusual.
Secondly, do research on what symbolism is in stories, why are symbols used and what are the meanings of symbols, for instance what is the meaning of a rose, what is the meaning of a cross, a flag, the moon..... etc.
Symbols are used by the authors to give more depth to the story, to mystify the readers, so you must try to find the hidden meaning of the symbols.
My strategy thus: read and reread, do research and draw conclusions based on your research