Others have addressed controlling sound within the room.
To prevent sound transmission to other rooms, the first thing to do is seal any air gaps in the walls. Don't overlook the electrical outlets.
Of course, that doesn't do anything about mechanical coupling of the walls (telegraphing -- sound hits wall, vibrates wall, wall makes sound on the other side). Anything you do to absorb sound will help with that. Other than absorption and sealing, there are a few common ways to reduce transmission through walls:
- Densifying -- place an additional layer of 5/8" gypsum wallboard on one or both sides of the wall. 5/8" is much more resistant to sound transmission than is 1/2". 1+1/8" of gypsum is even stiffer yet -- if you bond the sheets to the existing wall.
- Decoupling -- Build a second wall against the existing wall, staggering the studs relative to the existing studs to reduce transmission. Fill with acoustically absorbent insulation and cover with 5/8" gypsum wallboard.
- Decoupling option II -- remove the wallboard or plaster from one side and build a second wall with staggered studs. Fill with insulation and cover with 5/8" gypsum wallboard (or plaster, if you're masochistic). The disadvantage is the wall becomes a single large cavity, so may have fire rating implications. Check with an engineer. But since there is no hard connection between the opposite sides of the wall, coupling is almost nil.
While we're looking at this, is that crawl space access fire rated?
Disclaimer: I am not qualified to advise you on maintaining fire ratings or proper structural design. Consult with a qualified structural engineer before doing any of the above.
