a pot of water
Simple enough, right? Start out by laying your chestnuts on a kitchen towel (the towel helps keep things from sliding around), flat side down. Then, cut an X onto the bottoms of the chestnut with a very sharp paring knife, like so:
Put the chestnuts in a pot and cover them with water. Turn the heat on, and allow it to come to a boil. Boil for 5-10 minutes. Let the chestnuts cool in the water, until you are just able to handle them.
Peel the shells and skin from the chestnuts. It really is easiest to do this when they’re still warm. Discard any that are blotchy and weird looking on the outside.
I like to just eat them as is, but take a look on Foodgawker for some other ideas if you’d like to make something else out of them.