Born in Tokyo's Bunkyō-ku in the town of Akebono-cho, Miyazaki was the second of four brothers. His father Katsuji directed Miyazaki Airplane during World War II—a company owned by Hayao's uncle that manufactured rudders for Zero fighter planes. As a kid, Miyazaki drew planes constantly and became obsessed with aviation, something that would echo through almost everything he'd later make.
His mother was a big reader who wasn't afraid to question things, and Miyazaki has said he got his skeptical, questioning nature from her. She battled spinal tuberculosis from 1947 to 1955, which meant the family moved around a lot during those years. That period directly inspired My Neighbor Totoro—the film is basically set in that same era and features a mother dealing with the same illness.
High school was when things clicked for animation. Watching Hakujaden, often called the first-ever Japanese feature-length color anime, sparked something in him. But to actually become an animator, he had to teach himself to draw people, since he'd spent years drawing only aircraft and military hardware. He went on to Gakushuin University, where he graduated in 1963 with degrees in political science and economics. He hung around the "Children's Literature research club," basically the closest thing the school had to a comics club at the time.
Miyazaki landed at Toei Animation in April 1963 as an in-between artist on Watchdog Bow Wow. He quickly became politically active there, taking on the role of chief secretary of the studio's labor union by 1964. In October 1965, he married animator Akemi Ota. She stepped back from her career to raise their two sons, Gorō and Keisuke. Gorō followed his father into animation and filmmaking, directing Tales from Earthsea at Studio Ghibli, while Keisuke became a wood artist—he's created pieces for the Ghibli Museum and did the wood engraving featured in Whisper of the Heart.
His devotion to work has reportedly strained his relationship with Gorō over the years. Miyazaki has been clear that he doesn't want to build a dynasty of animators and believes his son needs to make his own way.
Content compiled by AnimeList.moe from publicly available sources.