The idea that witches fly on broom sticks stems form an old pagan tradition seen on Mid Summers. During the Mid Summer celebrations many pagans would take a broom, rake, or other tool with a long handle and mount it. Then they would run from one end of the fields to the other jumping and leaping as they went. This was to encourage the crops to grow taller. Onlookers that were not familiar with this practice thought the riders were trying to fly.
The witches flying ointment is another tradition that is misconstrued. This ointment was not meant to cause the broom or the witch to fly. The ointment contained compounds that when rubbed on the skin and was absorbed into the body caused hallucinations. This sometimes caused the person to feel like they were flying.
Personally I think that if one was to make a broom fly it would be an illusion mixed with the skill of levitation. As one would levitate and perhaps "fly" they would hold a broom underneath them self making it look as though they were riding the broom. The skill of levitation is not common and most who would active the skill through life long training would not waste their time doing tricks with it.