Basically, the professor is just going to carry on a discussion with a student or a few students about the material assigned for that class. Some professors employ different methods. I've had professors that will have 3 or 4 on-call students for the class. Those students will field all the questions, with the option of passing a question on to someone else if they don't know the answer. Other professors just randomly call on students. Some tend to focus on one or a few students for quite some time. Others jump around from student to student.
Generally, they'll take a case, Smith v. Jones, and ask, "What happened in that case?" A student will usually start with the facts and the procedural summary. Then, the professor might ask why certain facts were important to the court. Then, he might ask what was at issue. Then, he might ask about the case holding and reasoning. A good professor will ask why a court ruled the way they did and if that holding would be different if the facts were slightly different. Then, they may ask about a concurrence or dissent, if the case has one or both. Then, they might throw out a few hypotheticals that are based on the case but slightly different to see how the case applies to different fact patterns.
It's nothing to be afraid of. If you don't know, just say so. They can't do anything for you for not knowing the answer. I would try to answer the question before I defaulted to "I don't know". You don't lose points for wrong answers. I wouldn't worry about looking dumb in front of your classmates. They probably thought the same thing you did and just didn't have the balls to speak up. Besides, everyone makes mistakes. Just be prepared for class and try to answer the professor's questions intelligently. They are going to bring up a question that you cannot answer at some point. They want you to think on your feet, which is an essential skill for an attorney (at least a litigator). Mostly, they grill 1Ls to make sure that you are doing your reading and not relying on commercial outlines or commercial briefs. Lawyers have to learn to read actual cases. A good professor will ask you where in the opinion (page and paragraph) that you got your info. Just be prepared and be confident in your answers.