As the name may indicate, it seems that the best way to deal with these bugs is to squash them, or preferably their eggs before they hatch.
Last year, they ruined my entire patch because I didn't know if they were beneficial or not. The fact that all my squash plants were quickly being 'mummified' should have been a good indicator that they were definitely not benevolent visitors.
This year I have been awaiting their arrival. Not seeing them all through July, I thought I had escaped their yearly entourage. However, bright and early on August 1st, I went out and saw the beginnings of the 'mummification' of some leaves... Lo and behold, there were hundreds of tiny squash bugs on the backs of the leaves.
I knocked a bunch off into a bowl of water. The chickens and ducks enjoyed fishing them out of the bowl. Not a single bug was left. I found this tedious though and just started folding the leaves in half and pressing. They squash quite easily.
Some resources will tell you to spray insecticide. I have found that this is completely unnecessary.
Here are some good resources for info. and photos:
Ohio State University Fact Sheet
Will Taft Blog