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.}

If you're trying to ask someone's opinion about a film, then you can use either of the following sentences:

What did you think of the film? (I would also normally use the past tense.)
How was the film?

In the first case, I would use "what" in the same way that I would use "what" in the following sentence:

What was your opinion of the film?

I can imagine a situation in which you would start a sentence with "How did you think...", but it would be extremely uncommon:

* How did you think about the film? (Note the use of "about" instead of "of".)

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.

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? (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".

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.}