Expect the plumber to isolate sections of the system with valves and pressure readings, then use tools such as acoustic listening, moisture meters, or thermal imaging to pin down the spot. For a buried well line, they may trace the pipe's route across the yard before deciding where to dig.
Fixing a simple joint is often quick, but new piping, fixtures, or a backflow preventer can call for a Carver plumbing permit. Applications go to the Building Department on paper, and the plumber who holds the license books the inspection on one of the inspector's Monday, Wednesday, or Friday rounds.
In a mobile home, the plumber may need to open and reseal the underside covering to reach the pipe, and in a crawlspace, access can take as long as the repair. Ask how they'll close things up afterward.