Translation:How do you feel?
I'm sorry, but 觉得 doesn't exactly mean "think" and it's not really used the way we use "think" in English -- though, admittedly, whenever I've heard "你觉得怎么样" it's usually been in the same situation where, in English, we would ask "What do you think [about this]." If you check a dictionary, you'll see that 觉 means "perceive, sense, feel..." which is why it is used in 感觉.
Well, I can understand fully that it means feel by definition, however, I feel as though this is one the word in which the dictionary definition is not as popularly used. The reason I say this is because I also have commonly heard it being used as more of "What do you think about this" instead of " how do you feel about this?" or " How do you perceive this?". I think they should tell us that it can also mean to think or someone's thoughts about something.
This very thing is one of the limitations of learning a language outside of a country. What I mean is, when you're learning while immersed in the language and culture, you can pick up the feel of a word or expression because you use it and hear it used every day. In such conditions, you quickly understand that there are many things that don't translate cleanly into your native language, but it doesn't matter because you personally have the sense of the language.
On the other hand, when you're studying in a classroom or in front of the computer, you have to rely on the dictionary and what the instructor says are equivalents with your own language. It makes learning much harder and your speech winds up being awkward.
I also am studying the Pimsleur Mandarin audio course, and if 怎么样 is the same question phrase as in the audio course, then it is often attached to a suggestion to ask 'how about that?' As in 'Let's go eat, how about that?' So, I am not clear about the use of 怎么样 to simply ask how someone feels. I enjoyed everyone's discussion of this, and I hope that it will become clearer as I go forward.
That always depends on context and a bit on experience.
I would usually translate "你觉得怎么样？" as "What do you think?" or "What do you think about it?"
If someone shows you their article or painting or sculpture and asks that, they are obviously asking for your opinion.
If you are at a hospital and someone comes to visit, asking: "你觉得怎么样？" they could be asking for your health. Although, they could also be asking your opinion for their new hairdo - you have to decide from context. ;o)
For health/feelings, I would rather ask: "你怎么样？" = "How are you?"