The American Medical Association recogonized sleep medicine as speciallty in 1996.
The American Academy of Dental Sleep Medicine is a professional organization of dentists that fit patients with oral devices and thoracic equipment, or are involved with surgery for apnea and similar problems. They have a searchable on-line list of members (US) at http://www.aadsm.org/FindADentist.aspx so you can find a member near you. This can be useful for people specifically looking for this type of help.
You sometimes hear physicians advertise themselves as "board certified" in one area of medicine or another. The American Board of Sleep Medicine is the relevant board for sleep specialists. Doctors with the right experience and training and who have passed their exam are called "Diplomates" and can put the initials D, ABSM after their names. The ABSM has a list of diplomats at http://www.absm.org/listing.aspx so you can verify US doctors who claim to be certified. Unfortunately there is no search function on their website to allow you to find specialists near you.
Although most of their Diplomates are medical doctors, some are not, but instead have PhDs and are often working psychologists.
Additionally, some of the member boards of the American Board of Medical Specialties have additional sleep medicine certification programs for their doctors. Diplomates of these boards may get a certification through those boards. These include specialities in pediatrics, family medicine, and psychiatry.
The American Board of Sleep Medicine also certifies sleep technologists who administer polysomnograms and other tests. This is a relatively new certification and experienced technologists were certified. The ABSM is going to start giving exams to applicants for certification. They publish a list of their technologists at http://www.absm.org/rstlist.aspx.
The American Academy of Sleep Medicine (AASM) is a professional organization of people (not only doctors) involved in sleep medicine. They create practice guidelines for treatment of sleep disorders, and they are one of the organizations that puts out definitions of sleep disorders. They also sponsor research, try to influence sleep-related legislation, and publish the journal Sleep.
The British Sleep Society - a professional society, not much practical information on sleep
European Sleep Research Society - scientific organization