Purchase Homasote board at your local hardware store. At time of publication, it cost around $25 for a 4 by 8 foot piece, which can be used on each wall. If you have a large wall, you may consider purchasing twice as much. If you do not have it already, pick up a can of expanding liquid foam.
Place your Homasote board above the insulation in your room if you have not installed drywall yet. This will act as a layer between the joists and the drywall. Use your liquid foam to fill in any gaps that you can see.
Screw your Homasote board to the wall if you have a wall that is already constructed. Use several drywall screws along each side to keep it sturdy. To make this permanent, add another layer of drywall on top of the Homasote board.
Screw your Homasote board firmly onto the ceiling so that it has no risk of falling down. Use extra screws if necessary. This is only necessary if you wish to soundproof your room for sounds traveling upward.