Remember that sound is energy. When something resonates, sound waves, traveling in a straight line out from the source, will pass through walls and objects. There are two methods of soundproofing then: making it so the waves bounce off the walls and eventually lose energy or to absorb this energy.
Check for any holes made by pipes, ducts, air conditioners or whatever is making a gap in the room. Fill these holes with an adhesive agent that can absorb sound. A good one is Green Glue, which is a visco-elastic adhesive.
Absorbing sound in the walls and ceiling can be done with mineral wool insulation or acoustic foam. These work best when there is a reflective surface, such as fiberglass or concrete, behind them.
Look into sound barriers if the absorption method is unwanted. Blocking sound really revolves around two factors: density and weight. Now, a barrier sounds like a massive ordeal to install in the walls. However, barriers that reflect sound are also available and are actually rising in technology. One is a sheet of PVC vinyl material designed to reflect sound called dB-Block, which has astounding density for being so thin. This sheet weighs 300 pounds a roll but is only 1/10 inch thick.