There are many different reasons why you might want to soundproof a room. You may want to soundproof a baby's room to help keep outside noises away from your sleeping baby, or you might want a place to practice for a band without disturbing anyone. It is often thought that you should soundproof a room during initial construction but you can just as easily soundproof existing walls, possibly with even better results.
Install an extra layer of drywall. If you can afford to lose a little of the space in the room, hanging an extra layer of drywall is a great way to further soundproof a room. Drywall itself is somewhat soundproof. However, it is not enough to keep sound completely out. Having an extra layer will double the level of soundproofing. Leaving space between the two layers of drywall will further increase the soundproofing.
Blow additional insulation into the wall. Insulation can help a lot with soundproofing. Sound carries through walls by vibration. The more insulation is packed in the wall, the less vibration can occur. Insulation can be added from the attic into the studding of the walls.
Install special soundproofing foam. This material greatly decreases the amount of sound that comes through the wall. There are several ways that this foam can be installed. If you are handy and choose to take out and replace the existing drywall, you can install this foam in the studding of the wall before installing the new drywall. However, if you are simply going to add another layer of drywall, you can attach the soundproofing foam to the existing drywall before installing the new layer. Both ways are effective.