Secure several wood furring strips to your ceiling (with the number of strips dependent on the size of your ceiling area), using drywall screws and an electric screwdriver. The wood furring strips should measure about 1 by 3 inches and extend the entire length of your ceiling. You want the strips secured to the studs in your ceiling.
Secure soundproofing material to the wood furring strips, using nails and a hammer. Cover the entire surface of the ceiling with this material, nailing it into the wood strips.
Fill any gaps or holes between the soundproofing material and the walls with a good acoustic sealant. Allow the sealant to harden.
Mount a layer of drywall over the soundproofing material. Secure the drywall with drywall screws inserted through the drywall and into the wood strips. Maintain that 1/4-inch gap between the edge of the drywall and the edge of the walls.
Fill the gap between the drywall and the walls' edges with more acoustic sealant. Allow to harden.