The advice for a shop is pretty much the same as for any loud activity. There is a lot of research you can do on the internet for music studios, for example, that will apply. So, this is not specific to woodworking1.
The first question is what is your budget and how much work do you want to do? Ideally you would physically separate the walls from the floor, and the ceiling from the walls. This is a pretty tall order, though.
The most important thing to do is block as much air movement between the inside and the outside. Then you install sound blocking material between the basement and the rest of the house. The notion is that there is no single magic bullet; the only real solution is mitigation in depth by using multiple sound mitigation techniques together.
A serious modest approach would be something like:
- Clear all your tools from the walls and remove everything covering the walls and ceiling.
- Buy a case or three of acoustic sealant, and fill every crack and hole that allows air movement between the shop and the rest of the world. You cannot overdo this step, and no hole or void is too small to consider.
- Buy lots of sound insulation batts, or hire a firm to install blown or spray insulation into all the voids, making sure to get into every corner and nook.
- Cover with sound block rating wall covering of some sort, making sure to (in most cases) use multiple layers and follow the installation process for overlaps, joins, and things like outlets and light switches.
- Replace all doors and windows if necessary, and replace the air-seal around them.
You will probably have to separate the HVAC systems so the shop has its own heating and cooling, unless the rest of the house is ok with the sound coming through hot or cold air ducts. If you have non-ducted heating/cooling you already have a head-start.
A non-modest approach is to do all that, but start by building floating stud walls and ceiling that decouples the interior walls from the outside as much as possible, including (ideally) installing a floating floor.
A cheap-and-cheerful approach is to air-seal as best you can, and then use two layers of drywall, installing acoustically rated batt insulation in any significant voids. Seal the doors and windows (or cover them in semi-permanent baffling) and either put up with sound going through the ducts, or stuff them with some sort of safe baffling while you are in the shop.
1 That being said, I think wood shops are easier for sound management because at least we don't have to deal with as many high-energy low frequencies. This means that full surface separation as discussed is probably not strictly necessary except in the most specific cases.