Accidwntly voted for How do you think. "What do you think" is more common and natural. "How do you think" can be as well, if you want to know how they think something was accomplished. It just depends on the question you are asking them. 70% of the time you will be asking them 'what' they think about something if you want an opinion.
"How do you think" sounds like an incomplete sentence while "What do you think" is a complete sentence and sounds natural. As a native English (US) speaker, I have always used "What do you think" to ask for an opinion and never "How do you think".