First, I think I would say that native speakers do not learn most words by memorizing roots. The most common vocabulary is acquired by rote memorization in the first 12 years or so of life. Furthermore, about 26% of words in English are Germanic in origin, with a greater percentage among common words, and these roots are rarely taught, with most courses focusing on Latin or Greek roots.
That being said, when learning specialized and technical (read: Greek-derived and Latin-derived) vocabulary later in life, most native speakers do learn the roots. Many test preparation guides recommend some knowledge of roots for standarized tests such as the GRE or SAT, where testers can benefit from making educated guesses. Learning roots can help one remember words (again, most often of the technical variety). Example: many educated native speakers know that the word analgesia comprises the roots an-, meaning not or none, and algesia, from the Greek Ἄλγος, meaning pain. Nearly every native speaker knows that the root phobia refers to fear. If I asked a native speaker what algophobia meant, they would stand a good chance of guessing that it referred to fear of pain. Even if they did not, once they understood the meaning, it would be quite easy to associate it with analgesia in their mind.
So roots are useful, but most native speakers did not use them to learn their base vocabulary. Refer and defer share a root, but few could tell you what it means. (It comes from the Latin ferre, meaning to carry).
Best Answer
If you're trying to ask someone's opinion about a film, then you can use either of the following sentences:
In the first case, I would use "what" in the same way that I would use "what" in the following sentence:
I can imagine a situation in which you would start a sentence with "How did you think...", but it would be extremely uncommon:
I would interpret this question to mean: "What was the thought process you used in analyzing the film?"
@Matt points out that this sentence is unidiomatic, and I would agree. The only context in which I would expect to hear it would be a film studies class in which the professor was asking me to explain the thought process I used in analyzing a film. Even then, there are probably clearer ways to express this thought.