Both questions are correct, but they have different answers. What did you think of the movie? (Tell me your thoughts about the film) "I thought the story was terrible, and I didn't like the main actor" How did you think of the movie? (Tell me how you discovered the film) "I saw a review on TV and thought it would be a good film to watch."

'What do you think...' generally is referring to the contents of the thought. 'How do you think...' generally would be to consider the method of thinking. Between the two, 'what do you think...' is definitely used more often then the other. Example: A: What do you think about aeroplanes? B: I think they are very useful for travel. A: How do you think about shopping? B: I think in terms of need rather than want. Hope this was helpful! :)