There are three important things in the unconventional education of Woolf:
Her father, Leslie Stephen, was a man of letters, part of the English "intellectual aristocracy."
She never had a formal education but had unlimited access to her father's very extensive library; her brothers were sent to preparatory and public schools and then to Cambridge.
She decided at an early age that she would be a writer, while her sister Vanessa decided to devote herself to art.
Sir Leslie Stephen had a very successful Cambridge education and was don there before he got married. Males in his social class at the time went to Cambridge or Oxford for their educations as befitted gentleman. His sons followed him to Cambridge but it was not considered right to educate women.
It was an unusual move to allow such a young girl as Virginia to have full access to a library. It is clear from her letters and diaries that she made good use of this facility. She read copiusly throughout her life apart from times of illness. I am staggered by the number and range of books that she read.
She decided early that she wanted to be a writer so she is a great example of the old maxim that, Good writers come from good readers...