This is a very long subject that is a topic in itself.

There are different techniques for different frequencies, bass traps need big holes to absorb the long waves, higher frequencies need different solutions.
My brother has a tape measure with frequencies or wavelengths on it for quickly sorting out positions of speakers and sound deadening etc.
What they do nowadays is "Ping" the room by emmiting a test sequence and recording it with a special microphone, then they can do the required treatment. Bit extreme for a workshop though !

The simplest option for reducing higher frequencies like your machine is producing is something like a simple frame with an open weaved cloth stretched accross then a layer of rockwool behind it. This works and is pretty cheap. Position them around the router and it will reduce the noise a lot.

I was surprised at the sound reduction in my workshop when I built the walls up with two layers of osb and 100mm rockwool inside it.
As stated above rubber isolation feet will help as well.

Ollie