Some of the most successful criminals were successful because they were able to think like a cop, or have a cop's mindset. This really isn't too hard to do if you know anything about the profession, and that is becoming more and more easy with the types of programming on television these days. Having the mindset of a cop is beneficial in many other endeavors and not necessarily for devious pursuits.
Train yourself to look for criminal behavior. The best detectives are those who can instantly recognize the potential for devious behavior. They can easily spot those criminals who have put a "hiatus" on their behavior until the bystander has passed from view.
Be aware of your surroundings at all times. Look for opportunities for criminal action as well as self preservation. Be particularly mindful of potential areas of concealment, dark shadows, obstructed corners and idling vehicles for prolonged periods of time.
Read detective books. Especially read those written by detectives. Read true crime books written by cops. You will have a much better understanding of how they think and operate. You will easily catch on and adopt these methods.
Take a basic policing or criminal justice course from a local community college. Many colleges offer audit-only courses. You will not receive a grade for your work, but you will have the benefit of gaining all the knowledge and learning opportunities as a regular student.
Do not take your new-found hobby into the real world and attempt to be a citizen crusader. You will become the very thing you are trying to spot--a suspicious person. The police would be the least of your worries; the greatest would be that a criminal would spot you and that could be life threatening.