A hollow core door offers very little in the way of noise reduction. Just about every sound from one side of the door goes right through to the other side, where it can disturb a sleeping child or allow private conversations to be overheard. Although replacing such a door is the best solution, there are ways to effectively soundproof a hollow core door that will eliminate most noise transmission.
Attach a door sweep to the bottom of your door. A sweep is a strip of metal the width of the door. At the bottom of it is a loop of rubber that is plugged by a solid rubber core at each end. Fasten the sweep to the bottom section of the door with a screwdriver using the screws that come with it. Place the sweep so that the rubber doesn't quite touch the floor, but is as close as you can get it.
Wash the back of the door with dishwashing liquid and water using a clean sponge to remove dirt and grease. Wipe the door dry with a cloth. Allow it to further air dry until there is no moisture left to interfere with adhesive.
Measure the door with a measuring tape. Use this measurement to determine what size acoustical foam sheet you need.
Mark an acoustical foam sheet to the dimensions of the door. Lay it on the floor and cut it with a carpet knife. Place a yardstick along the cutlines as you work, to keep the cuts straight. Use thick cardboard under the area being cut, to avoid damage to the floor. Cut the foam slightly larger than the door, so that it will cover the cracks around the door. This helps to block out sound that might enter between the door and the door frame.
Apply the foam to the door. Generally speaking, there are two ways this is done, and which you use depends on the type of foam you have. The first way is to spray or roll adhesive onto the door. Put the mat on the sticky surface and press it into place. The other way is to peel the covering off of the adhesive side of the foam, and press it carefully onto the door. Follow the manufacturer's specific instructions for the acoustical foam that you have.
Seal the door frame with acoustical sealing tape. This will help to eliminate cracks around the door frame. This step may not be necessary if the foam sheet you've applied covers the cracks adequately, but in some cases this may be a necessary step. If sound is still coming through the door, add the sealing tape to form a gasket around the door, further blocking out noise.
Instead of attaching foam to the door, you can add a second door to the same door frame. Use a solid core, not a hollow door, and mount it in the frame with the hollow door, but place it so that it opens in the opposite direction from the first door. Be sure the new door fits the frame well and attach a sweep to the bottom for optimal noise reduction.
Some adhesives may damage the door. If you may want to remove the acoustical foam at any point, look for pre-glued mats that state the adhesive is easily removable. When cutting the foam, be sure to use thick cardboard for protection under it. Do not press so hard that you cut through the cardboard and damage the floor.