The difference between श, ष, स is mainly based on the position of tongue while pronouncing. It can get tricky and many school teacher don't even know the difference.

श (Ś) is palatal meaning the position of tongue is in the palatal region. Also, a gush of air which is called 'aspiration' comes out while pronouncing श. Example: शान्ति

ष (Ṣ) is cerebral meaning the position of tongue is cerebral. The back portion of the tongue touches the very back portion inside the mouth. Example: विष्णु

स (S) is dental meaning the position of tongue is close to the teeth. Example: सरस्वति

By becoming aware of the level of stress the tongue puts while pronouncing, one can easily distinguish the difference.