Sound isolation is science, not magic, and as such it is possible to outline a foundation of basic principles that define soundproofing in any given situation. There are just a few basic principles that govern the sound isolation of any wall, floor or ceiling.

Principle #1: Mass Mass impedes the transmission of sound in a simple way - it's harder for the sound to shake a very heavy thing than a very light thing, no different than saying it's harder to push a shopping cart full of lead bricks than an empty cart. However, to make large changes in performance you have to make very large changes in mass.

Principle #2: Decoupling Think of a typical wall. You have a stud with drywall on each side. If you hammer the drywall in room #1, that vibration will conduct through the drywall, into the stud, and directly into the drywall of room #2, where it becomes sound again. This is a very rigid, coupled wall, excellent for sound conduction.

De-coupling is very simply disconnecting this rigid connection by inserting a space or something resilient like neoprene rubber between one layer of drywall and the stud. Products are commercially available to do this such as resilient sound clips and resilient channel.

If you are dealing with new construction you should really consider staggered stud or double stud construction for rooms that need isolating. It is generally less expensive and higher performing that the commercial products mentioned above.

These techniques all function by inhibiting the movement of sound from one side of the wall to the other through mechanical paths (like studs or joists). Instead, the vibration has to pass through the air cavity between the studs, where some of it will be lost, and through the insulation/absorbing material, where (at higher frequencies) much of it will be lost.

Principle #3: Absorption This is accomplished with simple insulation such as cellulose, fiberglass and mineral fiber (wool). Exotic ($$) insulations are also available. Foams are not a good product to use for absorbing sound. Foam is excellent for thermal purposes, but not acoustic.

Installing insulation in a wall or ceiling cavity increases the sound loss due by eliminating/removing/destroying some sound. An important note is that insulation loses its effectiveness at very low frequencies. Put some fiberglass in front of a speaker at home and you'll hear the sound drop. Put that same insulation in front of a subwoofer and you might not hear any difference at all.

Insulation is important, but not very effective if it is the only technique used.

Principle #4: Damping This doesn't mean moistening your wall. To damp something is to reduce its ability to conduct a vibration. A steel pipe conducts sound well; it is not well damped. Drywall, subflooring and most building materials are not well damped. There are damping materials known as visco-elastics that can be very easily and economically applied between sheets of standard drywall and subflooring and are highly effective.

Principal #5: Sealing Make sure to caulk around all openings such as outlets and windows. Seal doors with weatherstrip. Install duct liner in your ducts. These all help to keep sound from entering or exiting.