Having looked into this myself ( I have a really awkward neighbour), there doesn't appear to be an easy and affordable way to do this if its to be really effective.
The most effective way seems to be by creating a " floating room" inside a room ( if that makes any sense) which would involve all sorts of boarding and soundproofing on wall bars, same on ceilings and floors, and even then noise would escape from doors and windows.
To help eliminate some noise, seals around a closed door maybe an idea even if its just a blanket on the floor, however the sound will vibrate through walls and floors. For this reason Im going to convert a brick building in my garden into a soundproof studio...seems my best option but not cheap ( luckily I have friends in building trade).
Some other members here have tried saxmutes, but I dont know anything about these other than sometimes practising with a duster in the bell of the sax which isnt ideal for me ( and probably not my neighbour).
Hope this helps and maybe other members might have some ideas.