1) Reciting the case. Sometimes a professor asks a question about the facts or the analysis in the case. They're trying to get students to identify and wrestle with the key parts of the opinion, and they're asking the student to remember what the opinion said. As a student, sometimes you just can't answer: You read the case earlier on, but you don't remember the part your professor has in mind.
What to do? If you really don't know the answer, I think you should just say so. You might say, "I don't recall that from the opinion" or just "I don't remember that." The alternative is to pretend that you know the answer. You could just guess, or you could start scanning the opinion in the unlikely chance you'll see the point in a second or two. But these alternatives usually don't work. If you guess incorrectly you'll probably look a bit silly, and everyone can tell when a student is staring at the page for a long time. Just be straightfoward and acknowledge politely that you don't know the answer.
2) Applying the rule. Sometimes a professor will ask students how a legal rule would apply to a hypothetical case. You know the rule and you understand the facts, but you're just not sure how the facts would apply.
What to do? I think you should explain your uncertainty. To the extent you can, articulate why you're unsure. You might say, "I'm not exactly sure how the rule would apply. On one hand, it seems that the rule would apply like this [fill in details]. But on the other hand, there's a detail that seems to point the other way because [fill in details]." Articulating why a hypothetical is hard is a really essential skill: It's the same skill you'll need to show on an exam to get a high grade.
3) Normative questions. Sometimes a professor will ask a student to take a position about what is the best rule. As a student, you might be unsure of what is the best rule. You'll have instincts about which rule you like, but you're just not confident that your instincts are sound.
What to do? Different people will have different advice here, but I think the best approach is to just pick a position and run with it. When a professor asks a normative question, the goal is to engage in a discussion of the pros and cons of different legal rules. The questioning should bring out those pros and cons, and a student needs to take a position for the process to begin. Sure, it may happen that the questioning reveals a problem with the initial choice: Upon seeing the drawbacks to your position more clearly, you may want to change your mind. But that's a good thing, not a bad one. It means that you're learning how to think through the consequences of different rules. Further, no one should be embarrassed by changing their mind after expressing a normative view. While a student may feel embarrassed to not know the facts, as it suggests lack of proper preparation, there is no shame in learning.
Anyway, those are my two cents. I trust readers will chime in if they disagree.