From Organic Gardening:
Find the eggs
Squash bugs lay eggs on the undersides of leaves in evenly spaced groups.
Get in the habit of scouting your squash plants for the shiny, yellowish brown to reddish eggs.
Also, keep your eyes peeled for the small, light gray or green, wingless squash-bug nymphs, which suck on the plant's sap, causing the leaves to wilt, blacken, and die.
Squish the eggs
Kill the squasheggs by gently rubbing them back and forth with your fingers, making sure you don't damage the leaf.
Squash-bug nymphs are also often present near squash-bug eggs.
If you see any squash-bug nymphs, be sure to squish them, too.