Your first year of law school, you will spend a big bulk of your time reading and briefing each of the cases in your assigned reading. This is super important. By your second year, you will probably be able to get away with using canned briefs (which are case summaries you can pull off the internet using your case name and citation), but your first year it's important that you understand HOW to properly read and brief a case, so you don't want to skip learning how to do this. You will need this skill come exam time and in the unfortunate event you get cold-called. Trust me.
Chapters in case books are generally organized according to a broad topic. For example, in Criminal Law, there may be a chapter on Homicide and in it there will be different sections for Manslaughter, 2nd Degree Murder, 1st Degree Murder, etc. Each section will illustrate important rules of law according to the most relevant and controlling cases available. When reading your cases, keep in mind that some of the stuff may not make any sense at first. Especially in subjects like Property law, some of the cases can be really, really old and use archaic language. Just hang in there and don't get stuck re-reading the same sentence over and over again. Your professor's job is to flush the cases out during class lecture. Also, don't skip over commentary, footnotes or dissents (although by 3L year, you won't really care about Scalia's dissenting opinions). Often times, you'll find pieces of helpful info in there that your Prof wants to discuss/question on. Use your highlighter and write all over the page, you'll thank yourself later when you get cold-called and need that info fast.
At the very minimum, you'll need to include the following in your case brief:
Heading: Case name, court name and date of decision
Facts: Relationship of parties and relevant facts to dispute
Procedural History: Describe what happened in the lower courts
Issue: What is the question in litigation? What is the court attempting to resolve?
Rule: Legal principle being applied by the court
Analysis: How the court came to their conclusion
Conclusion: Judgment/ court's response to question at issue
Write your brief out and take it with you to class. When you get called on in class, you're up! The Professor will ask you a series of questions about the required reading and you can use your brief to answer them. If he asks you something so specific you don't have it in your brief, revert back to your highlights and notes in your textbook.