Technically they can be picked and consumed at any time. But for best flavor and best long-term storage you want to wait until the stem on the fruit has dried and browned and the skin is hard. So hard that you can't score it with your fingernail.

Once harvested wipe off the outside skin with a cloth soaked in some warm soap and water and store in a cool, dry place. Root cellar storage is the best of course but few have one so you want to find a place that is as cool as possible but never freezes 40 degrees is ideal and with low humidity.

Dave

If you add just a little bleach to your cleaning cloth/water, you can prevent some mold/mildew from the outside of your squash.

Thanks everyone appreciate the help.