It depends. In my experience (I've worked at one for 2+ years now) if it's something huge (ex: she fried your hair, dye didn't come out the right color, cut it into a style that you didn't want/ask for, damaged your hair somehow, etc), then you'll more than likely be able to get your money back.
If it's something menial (ie: you said one inch, she took off 1 1/8th inch; you don't like how your hair falls now, etc) usually they'll try to fix it for you for free.
How did they mess up your hair?