Use shorter shutter speed. You will want a shutter speed of at least 1/60 of a second for most subject movements (except sport or any kind of faster movement). Something shorter than 1/250s would be ideal, but you need good light for that.
My P&S is a Panasonic Lumix FS15. Move off of Intelligent Auto (IA) and play with the menu a bit. Set Intelligent ISO to Off and use Sensitivity to increase the ISO. I don't think you can change the shutter speed on that, but your camera is more advanced than mine. My P&S, that is.