For performing, practicing and recording musicians, sound proofing and sound dampening measures are essential for a number of important music-making efforts. When space is limited and sounds must be kept either in or out of the practice and recording space, soundproofing foam is an effective way to insulate against sound. However, when this product is too expensive or just not readily available, a number of cheap, makeshift alternatives can provide effect dampening.
The bottoms of foamy or fibrous egg cartons (though not shiny plastic) imitate the shape of acoustic foam. This shape absorbs sound vibrations in the room by creating more complicated twists and turns for sound waves to resonate in, diminishing their energy. String together the bottoms of egg cartons and use them to coat walls and ceiling to take advantage of these properties. Attach each carton individually, or tack them together with duct tape into a single curtain and hang it in a manner that's fast to set up and remove.
Rolls of mattress foam work in a similar manner to commercial acoustics foam but tend to be cheaper and more readily available (especially if you have old or discarded foam). Soft materials of all kinds absorb and dampen sound, but rolled mattress foam has the advantage of being light weight and compact as well as large and wide enough to make for quick, easy covering of walls and ceilings. You can also use it beneath egg cartons for an extra layer of dampening effect.
Carpet, or carpet samples have both the benefit of being soft goods and of having a shape that traps sound waves in a manner similar to the egg carton shape, but on a smaller scale. If you have the opportunity to practice in a room with carpeting on the floor or on the walls, this will act as natural sound dampening, as well mounting additional carpet.
In a pinch, cloth goods of any kind will dampen sound, wherever they're located in a room. In a live space with lots of hard, smooth reverberating surfaces, just having cushioned chairs or a pile of clothes can influence sound. Maximise this effect by filling the space with rungs, curtains or thick blankets. This technique is most useful for neutralising smaller objects that may be contributing to the reverb in the room; for example, placing towels over a metal table will keep it from acting as a sort of sounding board and dampen the sound in the room.
Leaning old mattresses against the wall or on the floor of a space works both because it is a thick cloth and foam good, and because it effectively reduces the size of the room and the resonating space.