There are two main ways to prepare chestnuts so their shells and icky hairy skins come off with the minimal of fuss: roasting them or steaming them.
In either case, you'll need to cut an "x" or at least a "y" into the chestnut shell. This will let the shell loosen itself from the nut as it cooks.
How to Roast Chestnuts to Peel Them: Preheat an oven to 400°F, set prepared chestnuts in a roasting pan or on a baking sheet, and cook until the shells pull apart and the nuts are tender, about 30 minutes.
How to Steam Chestnuts to Peel Them: Bring an inch or so of water in a large saucepan, set prepared chestnuts in a steamer basket, put the steamer basket over the boiling water, cover, and steam until shells pull apart and the nuts are tender, about 20 minutes.
Wrap the roasted or steamed chestnuts in a clean kitchen towel, grab a seat, and get to peeling. Pull and snap off the shells, being sure to also take off the skin between the shell and the chestnut. When you're done, you want a pile of yellowish-white chestnuts.