The good news is that you can reduce the amount of noise that comes through a party wall in the way that you outline.
However whoever does the job must first establish that it's coming through the wall and not by way of flanking routes such as open windows or cracks or holes in the wall above the ceiling or below the floorboards.
So the first step is a proper diagnosis. I suggest you check out the project page. Click on the link at the top of the page that says: Click here for projects related to the topic Noisy Neighbours and look under sound proofing.
The projects will give you a good idea of what is and is not achievable.
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!