Before a hard frost, when the stem is brown and dry and hard and the rind so hard it resists pressure of a fingernail. Cut the stems from the vine, leaving them on the fruit.

Thanks. My acorns are pretty small but they are black. Will they grow any larger before harvesting or is it just a matter of hardening the skin now?

Les

Winter squash puts on its size first and most of the growing time is for ripening.

On our farm we grow tons (literally) of acorn and butternut. We try to pick the acorn as early as possible before the vines die. As soon as the acorns are exposed to the sun they will get burnt up. We lost half our crop a couple years because of sunburning. To know when your acorn squash are ready to pick gently lift the squash and check to see if the bottom of the acorn (the side that was resting on the ground) is orange. If it is, go ahead and pick it! All squash get sweeter after you pick it, so if you wait a week or more after you pick your squash it will be even tastier.
As for your butternut, they are easier to tell than the acorn because you don't have to look under the squash nor be worried about the sunburning. If the butternut is a good tan color (not greenish, whitish, or light tan, but a good tan color) go ahead and pick it. You can wait till the vines die with this squash, however they do get frosted easily so don't let it sit out in your garden too long!

Good luck!