Heres what I did...
I built a room, big enough for someone to comfortably stand in with a gtr. I had to build two walls, so on the outside wall, 5/8ths sheet rock, then the itchy pink fiberglass insulation, then another layer of sheet rock, then a layer of itchy pink fiberglass, with the itchy side turned out. I also put the itchy shit on the ceiling, then covered all the itchy shit with cloth, put down two layers of carpet padding, and some scrap carpet. I took one of the little single halogen tracklite looking lite things on the ceiling. For a door, I used an old outside doublepane glass door. This allows me to make fun of my nephew when hes trying to sing, and crack all his bandmates up. I got the outside door frame pieces with the built in insulation strips at home despot, and used an outside threshold with the squishy half round rubber piece. This seals against the bottom of the door, but will allow the door to close on a mic cable without hurting it(I use wireless headphones, so I dont have to worry about a headphone cable). I filled in all the cracks from my lack of carpentry skills with that aresol expanding foam insulation. After all this, the room is dead as a hammer. Its downright creepy to go in there and talk. No echo period. Just dead. Best thing is, I conned my nephews band into putting up the insulation.
Worst thing is, that I forgot the entrance to my attic was in that room, so now I cant get into my attic.
The fiberglass deadens it quite nicely, and doesnt cost near as much as the fancy foam shit. Not as pretty, but once I covered it with cloth, it worked, and looks fine. Just be sure to wear a mask while hanging the fiberglass. My free labor didnt and they didnt feel so well the next day.
And its dead....real dead.
If you have an existing closet, try just stapleing the fiberglass insulation to the walls, pink side out, paper side against the wall. Cover it with cloth, or youll be breathing fiberglass in there. Do the ceilling, and put something down on the floor, carpet, rug, etc.