Hey Stevenlouis,
as both Terry and hj have pointed out, line/leak detecting is an area of specialization even among plumbers. The equipment ranges from a few to several thousand dollars and requires a significant time investment to become skilled using it. A simple leak detection can take an hour or two, not including repair, and harder ones of course take longer. The good news is that copper is one of the easier piping materials to find leaks on, the bad news is the deeper the leaks are, the harder they are to find.
The typical process is to first locate and mark the waterline with a line locator, and then listen along the line with a ground microphone. If the results are ambiguous, the plumber may then try charging the line with compressed gas to increase the leak noise, or charge the line with helium or H2/N2 and use a gas detector to locate the leak.
Recommendations depend a lot on how old the line is, and how much effort/cost it would take to repair vs replace. Installing a new line is sometimes a better value, especially if you can provide some of the sweat equity.
Good luck!