NSSM logs messages in the Windows system event log. To open the event viewer, simply enter the "event viewer" in the Windows Start menu. In the Event Viewer, select "Event Viewer" ("Local") → "Windows Logs" - "Application → nssm" or "Event Viewer" ("Local") → "Custom Views" → "Errors and Warnings".
Also, make sure that you configure the log files for stdout and stderr when you install your service using NSSM.
The NSSM properties for installing the jar executable should look something like this:
: C:\Program Files (x86)\Java\jdk1.7.0_45\bin\javaw.exe
: C:\Program Files (x86)\Jars
: -jar C:\Program Files (x86)\Jars\my_executable.jar