Think of light falloff like depth of field - it's kind of the same principle. Keep your flash-to-subject distance short and your subject-to-background to distance long, so the subject gets the full brunt of the flash while the background gets a lot less. If your flash is on-camera, that means your camera is going to be very close to your subject too, so taking it off-camera would make things easier.
One tip I can recommend is once you have your settings where you want them, take a shot without the flash to make sure it comes out completely black. That way, when you turn the flash on, anything you see can only possibly be lit by the flash, and not ambient light (since your ambient-only exposure was black). That should help you make the adjustments you need to make to get the effect to work.
Also, it would probably go a lot smoother if you set your flash power manually rather than letting your camera do it, because depending on the metering mode it might try to expose the whole scene instead of just the part you want lit.