How can I tell if my significant other has been abusing substances?

Be observant. Signs of abuse may include frequently refilled prescriptions or hospital visits, track marks from needles on the skin and abnormal pupils (dilated/ constricted) or sclera (the whites of the eyes). Letting them know you are concerned and want to help rather than confronting them by accusation is the best approach to opening a discussion about the topic.
Change in habits. Change in habits, temperament hygiene can give a clue.