Install a thick carpet and pad on the floors of your home. Sound travels more freely through floors that are not carpeted. If you don't want to install a new carpet, a thick area rug can help too.
Put down a layer of mass-loaded vinyl on your floor. This thick, sound-absorbing material comes in rolls or sheets and greatly reduces sound transmission between floors. The vinyl works best when installed on top of open-cell polyurethane foam.
Secure any large objects, like speakers or your television, that vibrate or shake. Vibrating objects transmit sound into the room below.
Absorb some sound by placing fiberglass baffles on the walls or ceiling of the room. Baffles not only absorb sound, but are also a quick way to improve poor acoustics.
Place a white noise machine in your home. A white noise machine emits a non-specific sounds that cancels out other noise in the room.