This site shows you how to create a soundproof studio space by: insulating the wall with Comfortherm sound insulation material, following that up with a layer of Polysterene (similar to styrofoam) which is sandwiched between two layers of 5/8 inch fire resistant sheetrock.

It is recommeneded to use different width sheetrock layers, but we ended up using 5/8" sheetrock for both layers for added safety since it was fire resistant sheetrock, and Polysterene is a flammable material.

In order to completely sound proof a room you would need to follow the "room within a room" method and for the very best results, you would ideally purchase sound insulation materials that are extremely expensive... Before I started trying to make a soundproof studio space to play music in, I had some phone consultations with the sound proofing materials company Auralex. They gave me some ideas, their soundproofing materials would easily cost over $5000 - and this was out of my budget. So I found cheaper alternatives to all of Auralex's expensive soundproofing materials and was ready to create a cheap soundproof studio space.

You can sit around learning theory and trying to answer the questions "how does sound travel?", "how does sound work", or "how is sound produced", but let's simplify things a bit - one of easiest ways for sound to travel out of a room is through windows. So Soundproofing windows is very important. And of course there's soundproofing walls as well - We accomplished this by breaking the wall down and adding soundproofing material. And there's also soundproofing doors, which especially important from keeping noise from traveling to the rest of the house - to do this, we added a layer of Polysterene to the door and a layer of carpet, as well a weather strip around the lining of the door to minimize the amount of sound that escapes through the gaps.