How did Hedy Lamarr acquire scientific education?

Hedy Lamarr's father was a key inspiration, and she later learnt much from her first husband's social and business acquaintances. She was also highly intelligent, creative and motivated to help combat the Nazi and fascist regimes. It was her ability to see problems and come with ideas for solutions that marked her out.

Self-taught or self-educated inventors who learn from those around them (as opposed to in a classroom) are not as unusual as one might think: Thomas Edison is a notable example. In Hedy Lamarr's case, this started with her father. He

told her stories, read her books, and took her on walks in their tree-lined neighborhood and in the great park of the Wienerwald — the Vienna Woods. Wherever they went together, he explained to her how everything worked — “from printing presses to streetcars,” she said. Her father’s enthusiasm for technology links her lifelong interest in invention with cherished memories of her favorite parent.

Source: Richard Rhodes, 'Hedy's Folly: The Life and Breakthrough Inventions of Hedy Lamarr' (2012)

Another significant influence was Friedrich Mandl, a munitions manufacturer and her first (of six) husband.

As a young woman, before she emigrated from Austria to the United States, she married a munitions manufacturer and listened in on the technical discussions he held with his Austrian and German military clients.

Source: Rhodes

According to Lamarr herself,

“we entertained and were entertained by diplomats and men of high political position, makers and breakers of dynasties, financiers who manipulate the stock exchanges of the world.”

Cited in Rhodes

Once in America at MGM, Hollywood movies became her primary source of income, but she used her spare time to invent. She

...invented as a hobby. Since she made two or three movies a year, each one taking about a month to shoot, she had spare time to fill. She didn't drink and she didn't like to party so she took up inventing....In Hollywood she set up an inventor’s corner in the drawing room of her house, complete with a drafting table and lamp and all the necessary drafting tools.

Source: Rhodes

Her 'partner, the composer George Antheil, wrote in his memoir Bad Boy of Music of Hedy Lamarr:

Here, then, and at long last must suddenly come the true solution as to why Hedy does not go out upon joyous evening relaxations to which all Hollywood would only too willingly invite her, why her “drawing room,” sure enough, is filled both with unreadable books and very useable drawing boards that look as if they are in constant use. Why apparently she has no time for anybody except something ultra mysterious about which no inside Hollywood columnist has dared to even venture a guess. Believe it or not, Hedy Lamarr stays home nights and invents! I believe it because I know.

Cited in Rhodes

He also noted that she was highly intelligent, far more so than most of those around her, which was perhaps why she was bored by Hollywood parties. She enjoyed a challenge and even helped Howard Hughes with the design of an aircraft to help it fly faster. In an interview, she explained that the wings

...shouldn't be square...so I bought a book of fish and I bought a book of birds and then used the fastest bird ... connected it with the fastest fish and I drew it together and showed to Howard Hughes and he said 'You're a genius'

On a more general note on inventing,

Nino Amarena, the inventor and engineer, commented on the phenomenon in our discussion of his 1997 interview with Hedy. “More often than not,” he told me, “the inventive process follows a cascade of ideas and thoughts interconnected from previous concepts that for the most part lie separate, unconnected and unrelated. It takes a clear state of mind, which is usually someone thinking ‘outside the box,’ to suddenly or serendipitously see the connection between the unrelated concepts and put it all together to create something new.” In that regard, the process of invention is no different than the creative process in other fields. Scientific discovery proceeds the same way. So do painting and sculpture. So does creative writing.

Source: Rhodes