They basically set up shop in town and keep interviewing people until the suspect list is narrowed down to a handful, then they move in for the kill.
The family drove to Alaska when I was ten(1971). We stopped at campgrounds, and did the tent thing. One night, in northern BC, I believe, our campsite was robbed. We called the police, and holy crap, the Mounties show up. They made quite an impression. All we could do was follow a trail of discarded items up to a squalid Indian section of the town. Seriously impoverished, little kids looking out windows at the goings-on, probably like they did most days.