In his essay, Malcolm X refers to how he became knowledgeable and informed through what he calls "homemade education."
In fact, as you mentioned, Malcolm's essay is titled "A Homemade Education." This by itself is noteworthy: Malcolm came to learn more by teaching himself than by relying on others to educate him. Malcolm himself had dropped out of school in the eighth grade after his teacher contemptuously dismissed his ambitions to become a lawyer.
As time progressed, Malcolm came to feel his lack of an advanced education. He struggled to write proper sentences, and he experienced difficulty in understanding all that he read. In prison, he decided that it was up to him to make some needed changes. This was how his exploration into "homemade education" began. Essentially, Malcolm X began educating himself, first by taking hold of a dictionary from the prison library and then, copying pages out of the dictionary to improve his diction.
With each exercise, Malcolm found his comprehension improving, along with his command of the English language. To Malcolm, "home education" meant self education. After copying through the entire dictionary, Malcolm was able to explore other reading materials. Since he could now understand everything that he read, Malcolm found himself devouring other works that had until now, been off-limits to him.
Malcolm began reading books about ancient, modern, and American history; he also read abolitionist material, philosophical works, civil rights literature, and archaeological treatises about black history. Later, in conversation with an English writer, Malcolm X was asked where he went to college. Malcolm's answer was that his alma mater was "books, a good library." So, Malcolm X concluded that his own brand of "home education" propelled him beyond the level his previous teachers had envisioned for him.