Somehow they didn't get the memo: In order to do brainstorming right, you need to make ideas visual!
Still, this slideshow by Fast Company itemizes (and validates) the creative elements needed for innovation sessions.
[A facilitator] is the traffic cop of the session, and should be an outsider. An insider brings baggage that can inhibit the free flow of ideas. HR consulting organizations are one possible resource; if you are working with a design firm like IDEO or Continuum, they may be able to help.
If bringing in an outsider is difficult for some reason, the second best option is to bring in someone from a different group inside the company. Facilitators need to be skilled at group dynamics, able to read when the team is flagging or when it is hitting on all cylinders.
They have to be patient, yet willing to exercise discipline if one person can't stop talking or is becoming aggressive. It is more a matter of personality than formal training, but it can't hurt to bring in people to watch a well-run brainstorming session to see how it works.