We sleep about 1/3 of our entire lives, dreaming some of that time, and yet if we go much more than a week without sleep, we will die of sleep deprivation. Why any of these facts occur is still a mystery. Definite explanations for sleep and the accompanying dreams elude us.
Some institutions and professionals are interested in studying sleep and dreaming for various reasons, and this opens an opportunity to earn some extra income by volunteering as subjects for such study. By checking with psychiatrists, psychologists, colleges, and even mental hospitals, you might find employment while you sleep. Of course, if others are in charge of the research, you will have to meet their requirements and follow their schedule just as you would with any normal line of employment.
Remember that history is filled with examples of amateurs making great discoveries or advances in knowledge. If an income is not necessary to your sleep schedule and you like amateur sleep research, you might try it on your own. At the most basic level you can just have a notebook and pencil by a small table lamp and clock at the side of your bed. Record the date, time, and what you remember about your dreams. Perhaps something of value will turn up.
Some people have trouble remembering dreams. An assistant is a great help in such a case. The assistant can spend a part of the night if not all of it watching your eyelids for REM: rapid eye movement. This is a sure sign of the subject dreaming. Eye movement can be recognized even with the eyes closed. After the eye movement stops, the subject can be awakened and questioned about their dream, recording everything for study.
What will the study be for? If you are on your own, you can choose for yourself, but careful planning is still necessary. Study your subject before jumping into your research experiment. Are you pursuing knowledge of the paranormal; lucid dreaming, out of body experiences, astral projection, hypnosis, or extra sensory perception? You might be interested in relationships between dreaming and left or right brain activity. Research could be done in educational methods involving sleep or the amount of rest a student gets. The relationship between diet and sleep could be studied. Do certain foods affect sleep or dreams?
Whatever you choose to do, enjoy the experience of dream and sleep research. Your work could be compiled in a book for publication, and that could lead to an income later.