Sound travels better through air, so make sure your walls are well insulated and there is no empty space. Spray foam insulation is the most energy-efficient and best for sound deadening.
Before you close up the walls, wrap the electrical boxes with acoustical putty pads. You may need more than one to cover the entire box. This seal creates one less way for sound to transfer between walls.
The final step is to double-hang 5/8″ drywall and use acoustical sealant. The acoustical sealant won’t shrink, dry or harden, which will extend its life considerably over standard caulk. These final two steps will create an impressive barrier between rooms for little money.
An additional soundproofing tip: if a room houses a vertical drainpipe through the wall, use cast-iron for those pipes instead of PVC. With PVC drainpipes you can hear water rushing through on every flush, but with a cast-iron pipe it will be silent. Check out the video above for more.
Soundproofing Cheap Tricks [Matt Risinger (YouTube)]