Depends how much you want to spend and how far you want to go. You can add sound-dampening drywall (QuietRock is one popular brand) or you can simply hang "egg crate" mattress toppers on the wall. Those should dampen the sound, but your condo will look like a low-end recording studio.
Steve G's suggestion to use Quietrock is a good one. It is an excellent product. If you use it you will want to follow the manufacturers directions.
They will include calking around all the edges of the drywall to seal the air gaps. You can further improve it's performance by separating it from the existing wall by first installing metal hat channeling horizontally to the wall at the top, and bottom, and every two foot in between. By fastening the Quiet rock to the hat channel you will greatly improve it's performance by isolating the sound's vibrations in the air space, and break any direct solid surface that can transmit the vibration.
This technique will also work with 5/8" drywall, but not nearly as well as Quietrock.
I think I would use the egg crate mattress toppers, back with a light foam-core board (or even cardboard) and cover with fabric. You could get a really great wallpapered look and it would be light enough to attache without too much damage to the original wall. I made a 'removeable' wall for my granddaughter's room (in a rental) that also doubled as a place she could pin up her artworks, pictures, etc. It was a very small room and the bed had to be against the wall, so this kept the wall clean, too!