Dave said:

When do you pick butternut and acorn squash,

When the stems are very hard (they will be harder than twigs of the same
diameter) and the rinds are too tough to pierce with a fingernail. Ideally,
let them stay on the vine as long as possible without risking frost. Every
additional day adds flavor and sweetness.

and how are they best stored?

Acorn squash will decline fairly quickly for a winter squash during storage,
getting more and more stringy. They do not need curing as storage should
be fairly short-term -- eat them first.

Harvested squash should be set out in a warm, sunny area to cure before
bringing in for cleaning and storage.

Use squash with obvious insect damage or snapped off stems first. Cooked
squash can be mashed and frozen. (I use a food mill to process mine into
a uniform puree and freeze it in zipper bags.)

Harvested squash should be washed in a weak solution of bleach and dried.
I rub the butternuts with a bit of oil to help keep them from drying out in storage.
Store them in single layers with no fruit touching. Ideal storage conditions
would be 55 def F and moderate humidity. But even under less than ideal
conditions (70 deg and bone dry), butternuts harvested in October will last
to February and beyond. That means I can so put off the work of making and
freezing pureed squash until the mid-winter lull.

We are big fans of 'pumpkin' waffles and 'pumpkin' pies (made with pureed
butternut and buttercup squash). The squash I put up is much thicker than the
frozen squash you can buy and much, much tastier than canned pumpkin.
--
Pat in Plymouth MI ('someplace.net' is comcast)

Any technology distinguishable from magic is insufficiently advanced.
(attributed to Don Marti)