Its difficult to get good blurred backgrounds and bokeh with point and shoot cameras like the Coolpix S6300 due to their small sensors.
You may consider switching to a point and shoot with a larger sensor and good quality lens like the Sony RX100, or even better, switching to a interchangeable lens camera like a DSLR or a MILC. Prices of entry-level DSLRs and MILCs have dropped considerably and cost as much as high-end point and shoot models. You can consider models like Nikon D3100, Nikon J1, Sony NEX-C3, Olympus PEN E-PL1 etc.
With your current camera, it will be difficult to get this done.
At best, you can try this - switch to macro mode, go close to your subject (physically), keep the background at a considerable distance, focus and shoot.