We were asked to build a vocal/sound booth or room for the worship leaders at Saddleback Church in Lake Forest, California. Its purpose was primarily to block outside noise but we also wanted to deaden the sound inside the room. This is intended to be the place were they do their voice overs for music videos.
The overall size of the room was about 7'6" square so we decided to build it in our shop and then transport it to their recording studio.
Materials used in the construction included:
1/2 MDF for sheeting and battens
2" styrofoam insulation
1 " dense foam insulation
1/2 doug fir acx plywood for sheeting and battens
1 x 4 pine for framing
2" encapsulated rigid fiberglass insulation for interior sounding
2" aluminum angle for corner connections.
liquid nails adhesive for insulation
lots of screws and nails
laminated glass plate for the window

A similar room from a company that makes them such as "Whisper Room"
would cost about $15,000. We did it for much less. Your cost will largely depend on the size of the room and how many little extras you want to throw in like doors, windows and ventilation.