Forget packing blankets, egg cartons and non-acoustic foam: These do not work. That's just another Internet myth. actually you can find out almost all you need to know on Ethan Winer's excellent site.

Of course, compared with bare concrete walls, anything will absorb some sound, but anything thin is not going to do the job efficiently over the whole spectrum.

The preferred acoustic treatment material is Owens Corning 702 glass fibre. Here in the UK I use a mineral wool (not glass) of similar density sold for installing in walls to stop sound being transmitted through them. Either material has to be covered to keep loose fibres out of the air - you'll be clearing your throat all day if you breathe them in.

Acoustic foam is OK. It's more expensive but you can just stick it on the wall and leave it, and the sort that I bought from Studiospares in London several years ago is fireproof (in a fire it crumbles to dust but it doesn't burn)