The short answer: it is difficult to reduce the sound of most controllers. They're just pretty loud!
There are some steps you can take, although the effectiveness varies.
Using Thick Wood
Using thicker wood as a case material will result in a lower resonant frequency and add acoustic mass to dampen sounds.
After Construction / For Stock Controllers
Fill the Controller
Filling the controller with foam, cotton balls, towels, or fabric is a commonly attempted method, although it does not do a great deal.
Putting Pads Under the Buttons
Putting a thin material, such as tissue, cloth, or foam, between the black button housing and the clear button works to a reasonable extent, but changes the physical feel of the button, which some players may not like.
Ensure that the material you chose is not too thick, or it may prevent you from pressing the button fully.
Lubricating the springs with a plastic-safe lubricant (such as lubricants designed for mechanical keyboards, or silicone-based lubricants) will reduce the ping noise from springs. It won't do much for other sounds.