Find some fingerprints, talk to local places with cameras, basically do their job.
I'm not even so convinced that does much good.
Only one story so might not mean much in every case....
My brother in law once had his truck broken into sitting in his driveway. Scum Bag got a credit card and a ball hat, and I think a small handgun. Maybe some other stuff, don't remember.
Cops basically didn't do much...the way BIL tells it anyway, they seemed to have the attitude "maybe we'll get to it some day"
SO, BIL puts on his detective hat. Finds out that just after the approx time of the robbery, the card was used at a convenience store nearby. BIL goes and reviews the security cam footage, and the scum bag was wearing the hat when he used the card! Somehow he was able to even figure out who they guy was....but as far as I know the cops never did pursue it.