Leak and toxic atmosphere conditions perform isolation initially by the simple act of closing hatches and taking readings. In this case, they first closed the hatch at the front of the Russian Service Module and determined that did not stop the decrease in cabin pressure across the rest of the stack. That eliminated the Service Module. Then they closed the hatch between the FGB and Node 1. That resulted in a halt to the pressure decrease in the US Segment. This isolated the leak to somewhere in the Russian Segment, other than the Service Module.

That directed the crew to the procedure for isolation for a leak in the Russian Segment. That procedure has them use a manovacumeter called an MB (pronounced em-veh in Russian). The MB is a portable pressure sensor. It looks like an analog clock with a single big hand that indicates pressure. Using this device, they isolated the leak to the habitation module of one of the Soyuz.

An ultrasonic leak detector was then used to find the exact location of the hole within that isolatable volume. You can read about that device, here: Robert Frost's answer to How are the Ultrasonic Leak Detectors used on the ISS? Does the crew drill/train with them?

For more about the general process of leak detection, see Robert Frost's answer to What would happen to the crew of the ISS if a bullet hole-sized rupture occurred while they are freely floating around in it unprotected?