A number of Spanish witches admitted during their inquisitions that they engaged in night-flying. This is because witches would use hallucinogenic drugs to get high and make them believe they were flying. Their way of administering the drugs was rather novel even by modern day standards.
The hallucinogenic they used was called ergot, it came from a mould that grew on rye bread. In high doses ergot is fatal, but small amounts would lead to extremely intense experiences. Therefore, in order to avoid the risk of death, witches looked for alternative ways to absorb the drug quickly into their blood stream.
The most effective way, and the one with the least ill-effects, was through the female genitals. Witches would rub an ointment made with ergot onto the end of their broomsticks and quite literally sit on it.
So there you go - that's how witches fly!