All of those answers are wrong. Nitrous oxide and novocaine do not put you to sleep. Nitrous just calms you and novocaine is an anesthetic used to numb your mouth. You are talking about being sedated. There are many sorts of drugs that are used for people to go to sleep, the dentist I work for uses fentanyl, propofol, and versed. Hope that helps you out.
Most dental offices use an inhalation anesthetic called Nitrous Oxide (laughing gas). If it is an injection, it is probably Valium and Vistaril.