Two places: The work of Carl Jung and their own experience. Carl Jung and Sigmund Freud interviewed hundreds or thousands of patients with things happening in their lives, and part of the information received from them were their dreams. From the correlation between the things that were happening and the dream symbolism, they were able to put together 'dictionaries' based on the accounts of the people they interviewed.
On his own (perhaps with Dr. Freuds' help, I don't know) Dr. Jung also studied the myths of ancient societies and how they related to their way of life, and how 'modern' (or rather, their contemporary) works correlated to ideas that go beyond cultural. From that information, Dr. Jung compiled what he called archetypes, which are figures that symbolizes states of life or nature, and which also go beyond cultural ideas, and was able to put together what symbols meant in their proper context.
This is the source of what the good dream interpretation sites rely on, as opposed to places that use local mythology to explain dreams, or correlate all of them to some sort of religious or prophetic significance.
So yes, dream interpretation is a thing, and I think that if you stay away of religious hyperbole, it works quite well.