The answer to this question is found in Chapter 22 of this amazing novel. We are not given much information about the childhood of Miss Havisham, but what we do know can be found here, as Herbet dines with Pip and at the same time subtley offers him instruction on how to eat now that he is a man with expectations and has left his working class roots behind him. Note what he tells Pip:
Miss Havisham, you must know, was a spoilt child. Her mother died when she was a baby, and her father denied her nothing. Her father was a country gentleman down in your part of the world, and was a brewer.
Thus we can see that Miss Havisham was doted upon by her father, and having lost her mother at an early age, was left to be brought up as a willful child, indulged in everything. The wealth that her father made ensured that she grew up as a spoilt child. We can see this in the way that she acts as an adult and in the way she imperiously commands others and does what she wants. Of course, it is only towards the end of the novel that she experiences some kind of realisation of her own faults through her recognition of the suffering that she caused Pip.