and how much do they get paid and what exactly do they do?
Not sure how much they get paid though, and they study sleep cycles, and things like electophysiology of different phases of dreaming. They look at the mechanisms of dreaming, what influences it, and also sleep disorders.
The study of dreams is called oneirology, so maybe an oneirologist. However, people like psycologists and neuroscientists also study dreams, and there is a lot of overlap between oneirology anhd neuroscience.