Whether it's a home theatre, a nursery, or a noisy street, reducing sound transmission comes down to a few principles. Realistic expectations help — you can dramatically reduce noise, but completely silencing a room is expensive.
Seal the gaps
Sound leaks through any air gap — under doors, around outlets, at penetrations. Sealing these with acoustic caulk, weatherstripping, and a door sweep is the cheapest, highest-return first step. A solid-core door blocks far more sound than a hollow one.
Add mass
Heavier, denser assemblies block more sound. Adding a second layer of drywall — ideally with a damping compound between layers — significantly cuts transmission. Mass-loaded vinyl is another mass-adding option in walls and floors.
Decouple and absorb
For serious soundproofing, decoupling the wall surfaces (resilient channel or sound clips) so vibration can't pass straight through makes a big difference, as does insulation in the cavity. Inside the room, soft furnishings and acoustic panels reduce echo — a different problem from blocking sound between rooms.