You shouldn't see any green still lingering on the squash's exterior. A ripe squash is solid beige. Any remaining streaks mean that it's not quite ripe. The skin should also be free of brown spots ...
Finally, when you tap a ripe squash, it should sound hollow. Until you use the squash, keep it in a cool and dry place, but not in the refrigerator. Acorn squash can last about two months at room ...