Im not sure if the newest BSNES is new user friendly, it has a folder system that needs to be implemented in order to play games. Either manually or automatically or with the purify.exe and pressing "play game".
Manual is as so:
(game title).sys *folder*
-Save *folder* \\thats where the save states are stored.
-manifest.xml (not sure if it's created manually, or by BSNES on start up)
Byuu's step by step guide is right here, I just tried to make it even less technical.