To make a room sound proof, there are many steps to be accomplished. Besides having sound-proof, or close to sound-proof windows and doors, there are specific products that can be used to sound proof a room. After the framing is set up, either wood framing or steel framing, sound proof insulation is one product that can be used and it can reduce noise by approximately 70%. This certainly helps with noise reduction and would be the cheapest way to go about it. Besides reducing noise, let’s not forget that the insulation will help keep the room warmer in cold weather saving you money with heating and less hot in the Summer months saving you money in energy by not having your AC working so hard.
In addition, to make a room more sound-proof, there are sound proof boards that can be used/installed to make the room quieter. Also called Absorbing Acoustic Panels, they are much more costly than just regular blueboard/drywall. However, sure worth it depending on what you are trying to achieve.
QuietRock Sheetrock is a specialized product for sound proofing, which is known to reduce noise by about 80%, however, if the noise you are trying to block is impact noise (people walking for example), resilient channel and acoustic clip in addition to the QuietRock should be used. The material can be very costly. The work is certainly more laborious and heavy.