A case brief should be very (wait for it...) brief. It's a short outline of what happened in the case that you can use to refresh your memory in class and when studying.
It might be helpful for you to prepare a template that you then fill in for each case. You should include:
Heading: this includes the case name, what court the case is in, the date of the decision, and, if it's in your casebook, the page of the casebook (so you can easily and quickly refer back).
Parties: Identify the parties, both as plaintiff/defendant and also by their relationship to one another (e.g., Mr Jones: plaintiff/seller; Mr Smith: defendant/purchaser). This will help you keep them straight as you go through the reasoning/are questioned in class.
Facts: Give a brief (see? hehe) description of the important facts (in many opinions, the judge gives a statement of the facts before getting to the issue. In some opinions, the facts are scattered throughout the analysis). Sometimes the case will go into great detail about the facts, in which case you're going to want to figure out which facts were most important to reaching the decision. Sometimes the opinion will only give a few facts, and they might all be important. You'll probably figure out how to tell pretty quickly what's important; if a fact is directly referenced in the reasoning, you can probably assume that it's important.
Procedural History: This is what's happened (in court) in the case previously. Depending on what court the decision is from, this could be complicated (a Supreme Court case that's been remanded a few times) or virtually non-existent. You may also want to briefly note the reasoning of lower courts, if it's given and seems important.
Issue(s): This is the legal question that the court is deciding, and is often phrased as an is/whether statement. In many opinions, the author will come right out and say "the issue before the court is..." or something similar to indicate the issue.
Holding: The statement of law that comes out of the case. It's the answer to your issue statement.
Reasoning: How the court reached their decision.
Judgment: This will usually be something like affirming or reversing a lower court's decision.
Again, these should all be brief descriptions of what happened. Your goal is not to reproduce the entire opinion in a different format, but rather to have a tool to help you remember what happened in the case. Most briefs shouldn't be more than a page, but should hit the basics of what you discuss in class with respect to that case. Note anything that your professor spends time on that you left out of the brief, and pay attention to whether you're regularly including a bunch of stuff that you never discuss to revise your briefing technique (just because you don't touch on something in class doesn't mean it should've been left out of the brief, but if there's regularly a bunch of stuff in your brief that you don't talk about, it might not be worth your time to include).
A Google search should give you some examples of what a brief might look like (you are, of course, looking for case briefs, not legal briefs). There are also books of commercial briefs available; you might go to your bookstore and glance through them if you're having problems.
The basics I've listed above are by no means the only way to write a brief; unless you've been given specific requirements for your briefs, move things around/combine things/add things/leave things out in a way that's helpful/makes sense for you. As with everything in law school, the important thing is to do what works best for you personally.
Finally, a bit of unasked for advice that you should feel free to disregard: it might be a good idea to sit down with your family and make a plan for how you're going to find time for your law school obligations. Law school costs a lot, both in terms of time and money, and you need to make sure that you're going to get a return on your investment. Getting behind at the beginning of a term can leave you scrambling for the rest of the term and can make things a lot more stressful if you don't remedy it ASAP; catch up as quickly as you can. And you may want to reference a supplement of some sort for the topics that you've covered that you've missed out on because you've been unprepared.