I am building a room in my new house, the important essentials are;
1.0 Dimensions. There are ideal dimensions in terms of the room itself,
Ideal Room Dimensions
There is quite a bit of information about the appropriate dimensions on the net of course. This seems to be very important, square rooms do not make for good results.
2.0 Strength or "heft" to the structure, as well as lack of resonating materials. It all should be stuck together well and fixed together. This goes to such things as properly braced stud walls, and ensuring that any light material is well braced. Be careful about the connections to the main building strong and heavy/large can also result in good transmission of bass frequencies - just what you do not want.
3.0 Sound "proofing". The most effective means is to have a separate structure for the room. A room that is not attached to the main structure. A room within a room so to speak. This room needs to be sealed "airtight" as mentioned in the previous post. As mentioned there are proprietary systems but the best is to just construct "a room within a room."
4.0 The treatment of the room itself - appropriate reflection and absorption. The most up to date advice is to have the room "as dead as possible" More absorption than reflection. This can be an extremely large undertaking itself, and many $$ can be spent. My experience is to have it "cosy." Carpet on the floor and adequate absorptive material at the first reflection points from the tweeters to the listening position. Lots of pictures and other things to help break up reflections. A bit of experimentation with rugs works well.
The advice of two layers of plaster is good advice. If you cannot build/afford the two walls method then a single wall that is made from two layers of plasterboard over the studs and the cavity well insulated with an appropriate proprietary sound absorbent material is a good compromise. I have often done soundproof offices with this method and it works well and is economical.
Good luck. The subject is a minefield. There are products that claim marvelous results, and the old maxim of if it sounds too good to be true then it probably is, is good advice.