I don't know yet how good my character's psychic abilities are, but I don't want her to be a complete fraud. Is there some sort of middle ground? I am having a hard time figuring out her income as well. Over the summer I went to a psychic because my friend and I got caught in the rain and it was the closet shelter to us. It was a tiny little storefront and the woman was a complete fraud, but for $10 a reading it was fun. However, how would this woman possibly afford a downtown storefront at $10 a reading?
Tiny little storefront in a low-rent neighbourhood? Not on the ground floor, a walk-up 'office'? Landlord believes having a psychic on-site is good luck? Maybe the landlady gets a regular free reading? Psychic's family owns the building, actual tenants pay the bills, she gets the office and acts as manager on the side? She's got a pension, disability payments, settlement from insurance or lawsuit?
Then, if she's got one of those little ads in the classifieds, builds up a clientele, and does 'outside' jobs, she could do it. You and your friend went because it was raining, consider that you may have merely replaced a regular who stayed away because of the rain. How long did the readings take? $10 a head, 10 times a day, isn't bad. It's not like she needs expensive equipment like a dental office. Some regular furniture, maybe a deck of Tarot cards, or some smooth surface to scry with.
Then, if she can get hooked into the 'girls' night out' or bridal shower crowd, she's looking at group bookings, some of whom might become steady individual patrons, or refer other people to her. Occasional booths at fairs and bazaars would also provide a hit of money, as well as getting the word out.
As to how 'real' her abilities are, it probably depends on what your story needs. It could be anywhere from 'she's really good at listening to people, and perceptive, too', essentially a cold reader, to 'sometimes she just
knows stuff that she has no reason to know'.