I think he used sheet metal screws and a 1" washer. On mine, I used plain old drywall screws and 1" washers. However, the walls of my blind are made from a material called starboard and it's basically 1/4" thick plastic. For a 4x4 piece of foam, I think I used 3 screws on each perimeter side and a couple in the middle to snug it up.
It definitely cuts down the noise when my kids kick the wall or hit it with something. Add a piece of carpet or a rubber mat on the floor and it should quiet things down. I think you can get the rubber mats from tractor supply in the horse section. I got mine from Texas Hunter Supply when I bought my blind. I like the rubber matts better than carpet because we are always knocking drinks over and it's easier to clean up than carpet.