This is best done when the original wall is installed, but adding a second layer of drywall on each side and sealing around the electrical boxes will help. If you hang that second layer with the noise isolation clips, it gets a bit better. If you want even more, (this gets costly!) they make composite drywall panels that have a layer of lead sandwiched in between layers of drywall. There is also some special rubber caulk that you can use to attach the second layer of drywall. Solid panel doors help verses hollow core, and gaskets around the door along with a retracting, automatic sweep at the bottom can help. If there is a common HVAC duct, sound can travel through that, and that can get harder to fix without tearing a lot out.