Because sound travels in waves, the trick to soundproofing is to absorb or trap those waves until they dissipate. Shag carpet is best because the long fibres trap the sound, but any kind of old carpet will do some good.
Clear the walls of all decorations. Also remove unnecessary furniture from the room to help prevent sound from bouncing off of their flat surfaces.
Cover the windows. If all you have is cardboard, use that. If you have the means, insulate and drywall over the windows. Use fibreglass sheeting between the insulation and drywall if you can.
Cover the walls with a layer of carpet.
Cut cardboard and the remaining carpet into squares (6 inches is good). Leave an extra half inch on one side of each carpet square so that it is slightly longer than the cardboard.
Staple or glue carpet to both sides of each cardboard square. Let the extra carpet hang below the cardboard.
Staple the carpet-covered squares to the wall at a 90-degree angle. Separate the carpet flaps and staple each to the wall so that the carpet square juts out into the room. Arrange the squares in boxes, stapling four in a square against the wall and stapling their sides together. Continue adding these boxes until the entire wall is covered. The effect is that the sound goes into the carpet boxes, bounces around and dissipates. I was in a room like this where the sound literally stopped when it left your mouth, and you could hear your own heart beating.
Covering the floor and ceiling with carpet will also help your soundproofing efforts. For an even better effect, create the carpet boxes on the ceiling and floor as well (you'd have to have a mesh walkway above the floor to walk on). If you don't have enough time or carpet to make the squares, apply one layer of carpet to the wall as waves (staple once every 12 inches, letting the carpet bubble up from the wall in between).
Carpet alone will dampen sound, but for true soundproofing you need fibreglass sheeting or soundproofing foam inside the walls.