If you're trying to ask someone's opinion about a film, then you must use "what":
What did you think of the film? (I would also normally use the past tense.)
One way to think about it is that you're asking for someone's opinion, and the following is clearly correct:
What was your opinion of the film?
You can ask questions that start with "How did you think...", but it would mean something very different:
How did you think about the film?1 (Note the use of "about" instead of "of".)
I'd expect this type of question in a film studies class. This question is asking someone to describe the thought process they used when thinking about the film. It's a very literal use of the word "how" to mean "in what way".
1 @Matt points out that this sentence is not very idiomatic, and I agree. It's a specialized question that would only be asked in very narrow, uncommon contexts (e.g. academia). It should not be used in everyday speech.