It depends on what you want to do with it, eat it soon or keep it for long term storage. Technically they can be picked and eaten at any time after they reach the size you want but they won't keep for long and the more you let them mature the better the flavor.

But since most grow winter squash for storage purposes if that is the goal then you want to wait until the stem is brown and dry and the skin, the peel, of the squash is hard. That is usually in late August into Sept. depending on where you are located. Some use the thumbnail test - can't dent the skin with your thumbnail. Others use the pigtail test - the small curly "pigs tail" vine right above the stem is dry and brown.

Dave