You can receive credit for detecting (and maybe preventing) 20 crimes. You will be alerted to their existence randomly, with a pop-up notification. You can press a button to mark the general area where the crime is anticipated on your map.
Once you expect a crime, head to that area and look for the perpetrator or the victim. You will sometimes need to tail an individual (innocent or otherwise), or sometimes just maintain surveillance. Eventually, a criminal and victim will get together. If you aren't seen, the crime will go forward.
You can see a yellow bar increasing, and you will be prompted when it is time to intervene. Then you can rush forward and take action. Shoot or perform a takedown and bust the criminal. You'll gain some experience points and a boost to your reputation. If you fail to prevent a crime, don't worry; you'll find another random opportunity soon enough...
NEXT: Fixer Contracts