Those automotove sheets are the "constrained layer" I was talking about. Cheap ones are tar based and will stink. Better ones are a butyl compound. Off brand work as well as the grossoly overpriced Dynamat. They have two functions. One is to add mass and so lower the frequency of resonance. The other, to a lessor extent, is to convert some of the sound to heat. If you go to industrial supply houses, you can get even higher performing materials. Boat supply houses have materials they use in engine compartments.
You don't need to cover the entire panel. If it is, say 14 square, then a 12 x 12 sheet works fine. Any extra and trim, slap on over top.
You reduce noise depending on the source. Belts are a big one. Blades/cutters, sheaves, and basically anything spinning in air will make noise. In the real of hobby or small shop woodworking the only solution is to wear hearing protection. In large scale industrial shops, machines may be enclosed and fed robotically to reduce the noise on the floor.
Usually, one method of reducing noise is to seal the cabinets where the noise is generated. That won;t work on woodworking machines. Holes for the blades, holes for cooling air, holes for dust extraction.