This article is from the Food Preserving FAQ, by Eric Decker email@example.com with numerous contributions by others.
From: ZebCook@pacbell.net (David Cook):
It's absurdly easy. Either take a needle and thread and string the chiles
in a bunch near the stem of each, then hang in the sun. After a week or so
they'll be nicely dried and you can break them off as you need them. This
works particularly well for thin-walled chiles, like cayennes. Or, spread
them on the rack in your oven, set it to just warm and prop the door open.
Leave them in their overnight or longer until they're done. If the chiles
are thicker, you might split them before drying.
Finally, get a dehydrator and dry them in it.
Personally, I favor the sun method. It's cheap, doesn't tie up the oven,
and strings of chiles belong in the kitchen (at least in mine!)
[Nylon thread works very well, strong and doesn't fray. This procedure
works just as well with morels, ceps and other edible wild mushrooms--just
know your mushrooms. -LEB