Cheap soundproofing a bedroom wall?

http://www.ikea.com/us/en/ideas/201542_idbe01a/

You can buy sheets of inch thick Styrofoam and lightly tack them to the offending wall. Then buy long curtains , fabric or flat sheets and hang a rod from wall to wall (the rod can be pvc pipe to run through the casing of the curtain) to hide the Styrofoam.

I had this same problem and I solved it by stapling polyester foam batting to the common wall. Then I purchased felt from my fabric store in the color I was going to paint the other three walls. Felt comes in 72" width, so I only had to sew two pieces together to cover the wall. I stapled the felt over the batting along the edges and then glued decorative trim to cover the staples. Heavy lined drapes, carpeting and area rugs also tend to quiet a room.

Anything "spongey", soft, foamy, etc will help absorb sound. Two of the cheapest and most effecting things I know of are styrofoam and "egg crate" style packing foam. Both you can find for free around somewhere that gets a lot of large deliveries. The tricky part is attaching then evenly and making sure they cover the wall completely. And they can look bad, so it's best to have some sort or decorative fabric.

if I had a little money to spend, i would a wide swath of dense foam to cover the wall, then hang decor-appropriate rugs on the adjacent wall and something like lighter throws on the other walls.

You can also line the walls with furniture to absorb sound

Get a few sheets of 1/2" thick rigid sound insulation board to do the offending wall, and cover with fabric or that removable wall paper at home depot

If you are renting or wanting protect your walls , use command strips to put up carpet, foam, old comforter whatever you have that looks acceptable and decorative You might try cardboard boxes covered with wallpaper or posters.

Custom fitted noise blocking ear plugs. About the same cost of materials of any of the above ideas, no labour involved, and totally transferable to any space.