If a nuclear weapon is tested, will we know?

Yes, the Preparatory Commission for the Comprehensive Test Ban Treaty Organization has the technical capability of distinguishing a nuclear explosion from, for example, an earthquake. This agency has established a series of monitoring sites for seismic, hydroacoustic, infrasound and radionuclide monitoring. All data is both analyzed in the International Data Centre in Vienna and shared rapidly with member states. Their excellent website with a clear explanation of the verification regime now in place can be found at: ctbto.org

Go here for videos on the different types of verification methods that are used to ensure we know with certainty when a nuclear explosion has occurred.