Hi Anya, What do you think? - is a question asked to someone to give his reaction to what was just said. "What do you think about this situation?" How do you think? - alone, it is not a legitimate question. It does not make sense at all. Unless, of course, you have a context: "How do you think we should go there?" - "I think we should go by car". :)

I would not use "How do you think" unless it is followed by a verbal phrase: How do you think you can do something? In all other cases, I would use "What do you think?"

"How do you think?" это такой же русизм как "How much time?" вместо "What time is it?"