The things I just mentioned—cookies, walnuts, dried peppers, popcorn balls, whole fruits—are the easiest, and most common, edible ornaments. When you're whipping up a batch of cookies, add a dozen or so extra for your tree. Brushing gingerbread or sugar cookies with egg glaze before baking makes them shiny and especially attractive. Tie a piece of natural twine around the stem of an apple (make sure to choose an apple that your tree limbs can support). When you're making popcorn balls, insert a piece of string into your handful of popcorn mix before you mold it into a ball shape; that way you don't have to thread a piece of string through solidified sugar. Thread a string of dried red peppers and garlic together with a needle and thread, and use spices, such as star anise or cinnamon sticks, in creative ways, as well.
Depending on how long they're hanging up, cookies and popcorn balls may get too stale to enjoy after your holidays have passed. If that happens, cover them with peanut butter and birdseed for the birds.