The handle of a broom, to which the bristles are bound.
Witches fly on brooms, but we call these witches' brooms 'broomsticks'. This is in part because the broomstick is the most important part for flight (a broomstick can fly without the bristles, but the bristles cannot fly without the stick), but even more importantly, magic wands and staffs can be disguised as broomsticks, which is especially important in times of persecution. The witch sits on the broomstick (usually sidesaddle), with the bristles towards the back. It is usually best to fly at night, when the power of the moon can help you, and muggles can't see you.
"...in rifleing the closet of the ladie, they found a Pipe of oyntment, wherewith she greased a staffe, upon the which she ambled and galloped through thick and thin, when and in what manner she listed."
-- From the official report on the investigation of Lady Alice Kyteler, 1324.
In 1973, the illustrious Michael J. Harner put forth the theory that 'witches' weren't literally using their broomsticks for flying; instead they were using them to apply a paste* made from hallucinogenic plants to the vaginal mucous membranes (for more effective introduction into the bloodstream). This would also help explain why the witches' sabbat is so often reported to be sexual in nature. For more on this, see his book Hallucinogens and Shamanism.
Of course, we all know that's not what's going on. Thanks to popular accounts of witching and wizarding life** (e.g. Harry Potter, the Discworld books, and my favorite, Witch Week), we know that is possible to ride on a broomstick without making a covenant with the devil. In fact, most of the work in broom riding seems to be simply in finding a magic broom, and hanging on tightly.
If you wish to make your own aviation grade broomstick, you will need some birch twigs for the bristles (birch is a healing wood, and can be used to drive out evil spirits), and a staff of a wood for which you feel affinity. Some popular choices are:
- Ash (balance of power, strength, wisdom and spiritual knowledge)
- Hazel (divination, poetry and healing, a favorite of druids)
- Hawthorn (cleaning and psychic protection)
- Rowan (deflecting spells, protection from enchantment, enhance strength and courage)
- Willow (a connection with the moon and the otherworld)
- Blackthorn (protection against evil, strength, and courage)
The birch twigs should be dried in the sun and bound to the broomstick with strips of willow
bark. (If you are serious about making one yourself, you should consult Wertperch's Besom
node). Once all is ready, wait for a moonlit night, and fly!***
* This paste thing is not completely out-there; there are a lot of reports of witches flying after applying a paste to themselves, animals, sticks, or etc. Broomsticks are actually in the minority of pasted objects. If you are in fact a Devil worshiper, you can make a paste out of the fat of unbaptized young children (among other things) which will allow you to fly. But that's for bad witches. Good witches don't do this.
** Disappointed that there isn't more about Wicca and the symbolism of the broom and besom? This is the broomstick node; few wiccans refer to their brooms as broomsticks. Broomsticks are the things that fly through the air, ridden by people with black pointy hats. They are related about as much to the Wiccans as they are to the devil worshipers who cooked up the baby paste (maybe about half and half?). The broom node touches lightly on the magickal uses of brooms in the pagan and Wiccan traditions.
***Expecting to find the secret of magical flight posted on E2, were you?**** Well, sorry, but my sources stop just short, and therefore so must I. You might try making a brew out of henbane, belladonna, and mandrake, but be warned that this is poisonous and hallucinogenic, and should be applied to the broom, and not yourself.
**** Um... Wertperch has directed me to How witches fly, where the secret to magikal flight is indeed posted on E2. Never underestimate Everything.