Experts use a combination of methods to identify nuclear weapons tests. You can separate them into a few key categories: seismic analysis, scanning for radioactive gas, and listening to sound waves underwater.
There are hundreds of sensors around the world designed to pick up the seismic activity associated with nuclear weapons. From decades of research, we know that nukes set off underground create vibration patterns that can be easily distinguished from earthquakes, drilling or other activity. But countries like North Korea go to great lengths to minimize the disruption their tests cause, making it harder to confirm using seismic analysis alone. What the network of sensors is really good at is helping to triangulate, or pinpoint, the location of a nuclear test.
One of the telltale signs of a nuclear explosion is radiation. If the testers are trying to cover their tracks, there may not be large pieces of radioactive evidence. But there may be radioactive gases that can seep through earth and rock and escape into the atmosphere. So in the wake of a suspected nuclear test, watchdogs will "sniff" the atmosphere for xenon, which doesn't bind easily to other elements and makes it easier to link to a nuclear test. By analyzing wind patterns, experts can even work backwards to find the source of the xenon they've detected.
Much like the underground seismic sensors, there's also a network of underwater microphones designed to listen for nuclear-related vibrations. Because sound travels incredibly well underwater — this is the same logic that powers sonar — experts can pretty easily identify sudden, violent disruptions against the backdrop of ordinary ocean noise.
At the moment, however, all we truly know is that North Korea claimed to have blown up an H-bomb, that scientists detected a 4.9-magnitude seismic event and that Japan has sent jets to sniff around for radioactive isotopes. Investigators may not find any xenon gases to speak of, as was the case after North Korea's test in 2009. In 2013, researchers could only pick up inconclusive amounts of the material.