Buying Chestnuts:
After picking, chestnuts slowly dry out and shrivel. Choose nuts that are heavy for their size with shiny, smooth shells. Give a squeeze to check that the nut inside is plump and full.
Storing Chestnuts:
Freshly picked chestnuts start off quite crisp and become more tender and chewy over the following days or weeks before deteriorating to a dry and floury texture. Storage at a cool temperature (e.g. the refrigerator) slows the aging process.
Preparing Chestnuts:
Peeling chestnuts is a task to plan for when there's something good on the radio; attempting the job when you're in a hurry is likely to result in swearing and a long-standing hatred of a very fine nut.
Cut slits (or crosses) in the shells and part-cook the nuts either by roasting for 15 minutes or boiling for 20 minutes. The shells will now be fairly simple to break open. Removing the brown membrane on the nut is a fiddlier task (easier performed while the nuts are warm) and you will need to break open some nuts to get at the skin in the crevices.
Shelled and peeled, chestnuts can then be cooked according to recipe requirements (for mashing or pureeing they should have the consistency of cooked potatoes -- test with a skewer).
Chestnut Tidbit:
Ham from pigs reared on a diet rich in chestnuts is highly valued in many areas of France, Spain, Italy and particularly Corsica (home to an annual chestnut festival in December).