As you can see, there are seismic station for detecting underground tests (the signal differs from earthquake signals if you look at stations around the world), acoustic and hydroacoustic stations for detecting tests in the atmosphere and oceans, and isotope detection to differentiate between any kind of explosion and a nuclear one (which leave the same signal in the other detectors).
The stations have a fantastic global coverage and have been measuring for quite a while. The data set is now also given to the scientific community for all sorts of purposes.