There are fellowships in sleep medicine that you can start after completing a psych residency. I'm not sure but I think that you might be able to do a fellowship if you have trained in another field like pulmonology. From what I have heard about the field it is fairly competitive to get into.
One thing that sleep med doctors do is analyze sleep studies from patients who come into the sleep lab and basically spend a night hooked up to EEGs, etc. to diagnose disorders such as sleep apnea.
Given the epidemic of obesity in our country, there are plenty of patients with sleep apnea and more than enough busy to make the sleep lab at my school almost impossible to get an appointment in.
