A plumber will usually isolate parts of the system to narrow down where water is going, then use tools such as moisture meters, thermal cameras, or listening equipment to pinpoint it without opening walls at random. In a well home, they'll also check that the pressure tank, switch, and check valve aren't causing the pump to cycle on their own.
If the leak is in the buried line between the well and the house, finding it may involve tracing the pipe across the yard. Once the leak is found, the repair might be a single fitting, a section of pipe, or, for widespread pinholes, a plan to repipe parts of the house.
Pipe repairs and repiping usually require a plumbing permit from Rochester's Building Department, and the plumbing inspector arranges the inspection directly. If corrosion is the cause, ask whether a water test or treatment should be part of the fix.