The prelims are big exams all prospective PhD students are made to suffer through for whatever reason. Let's take a few minutes to go over the facts.
The prelims consist of 3 exams, each of which is 4 hours long, covers 3 different subject areas of the core curriculum, and (thankfully) are given on 3 different days. The exam is offered once a year in January. The first day is "Systems Day" and covers Operating Systems (663), Architecture (662) and Networks (650). The second day is "Software Systems" and consists of Artificial Intelligence (681), Compiler Construction (672) and Programming Languages (670). The final day, and typically the bane of all grad students, is "Theory Day" and has Algorithms (621), Logic (604) and Theory of Computation (601). Hefty stuff, ain't it?
Now, I've listed the order of the days as Systems, Software, and Theory. That's usually the order they're given in. It may change from one year to the next. You will, however, be told the order of the days a few weeks before the exam takes place.
Each day has 12 problems on it, 4 from each area. Each problem is worth 25 points. You're asked to answer any 6. After you're done, two faculty members will grade your work. If they differ by a certain amount, they we will be asked to reconcile the difference. Your score is the average of the two grades. To pass the exam, you need a 70% on each day.
What happens if you don't get that? Well, you fail and take the exam again next year. You may be able to get around this. If you pass 2/3 days with no question (e.g. you're "well above" 70%), and you've at least wrote something intelligible on the third day, then you will not have to take those 2 days again next year. What's the definition of "well above"? Difficult to say. It depends on how hard or easy the exam was for that given year. I think it's fair to say that if you hit 80% then you're "well above" the needed score. If you've only passed 1/3 days, then well, sorry, see you next year when you take all 3 days again.
Now to tell the truth, you may not need exactly 70% to pass, but if you get it there's no question. If you get a little below it, you could be asked to go take a course, get a B, and they'll consider you passed for a given day. How much is a "little below"? Well, again that is somewhat subjective as it depends on how hard or easy the faculty think the test was. It also depends on how good a grad student you've been. If you've done well in courses, maybe a little research, and didn't annoy the secretaries (you did read the first Bash right?), then the faculty will be more inclined to grant you these little conditional passes.
Enough facts. On to more interesting things, like test strategies. Since you're only asked to answer 6 of the 12 questions on each day, you could very well ignore one whole area, so long as you're really strong in the other two. I don't really recommend counting on this since it's possible you'll get some questions you don't know how to answer in your "strong" areas. But, you may have no choice if, for example, you didn't take a particular course. Remember, you need to take courses from each core area at the 600 level, but for MS degrees you also have to take 3 800 level courses. So the first time you take the prelims, usually after 3 semesters, you may not have had all the courses.
A perfectly legitimate strategy is write off one of the days as a failure, but study hard for the other two. Remember if you pass 2, you may not have to take those two days again next year. You should try to pass all 3, but if you find yourself running out of study time, and one of the days just isn't clicking for you, then studying for the other two and making sure you pass them, may work. However, bear in mind the discussion above. You would have to do really well on the two days you concentrate on and write something for the third to nail this path down. If you're close to the 70% mark on both days they may not grant this little pleasantry. Again, this strategy should only be used if you have no other choice. It is always better to pass all three days than it is to have to take one day again next year.
The faculty, despite making you take the exam, do try to make it fair. Usually 2 or 3 faculty make up the questions for each area. One of those faculty is likely to be the one who last taught the relevant course (the only time it wouldn't be is if the person is no longer here, on sabbatical, or was only part time to begin with). That person will very often use their final exams as a basis for questions. Thus, it's in your best interest to get a hold of the most recent final and look it over. Now, because of this, some faculty will not give you a copy of their final. Fair enough. But that doesn't preclude you from bugging someone who was in the class to find out what was on the final.
Ah, now we come to it. You've decided to take the exam, you know some strategies for getting through, but the important thing is how do you study and prepare for it?
I can't tell you.
I'm not holding a great secret from you or anything. It's just that I can't tell you how to study because it's different for different people. You know (or should know) how you best learn and how you best prepare for exams. Do that. Basically, you can think of it as preparing for the final exam in each of the subjects. What would you do to get ready for that? While I may not be able to tell you exactly how to study, I can give you some ideas and tell you how other grad students have done this.
The first is to get a copy of the old exams. I'd recommend getting your hands on the last 3-4 years. The topics each course covers, and thus what appears on the exams, changes over the years, so I wouldn't go back too far, or at the very least, I wouldn't pay as much attention to exams from 6 years ago as I would for exams in the last 2-3 years. The department keeps previous exams, without solutions, on file. Find them and copy a few (keeping in mind the department's use of copier policy). Off hand, I don't know where they're now kept. They used to be in Smith 214 before that became lab space. As always, if you don't know, then go to the great Keepers of all that is Knowable, the secretaries and politely ask them.
Once you've gotten a hold of a few exams, what do you do with them? Well, similar topics come up year after year. So look over the exams to find out what types of questions are being asked, and make sure you know the ones that keep popping up. For example, on theory there is usually a generalized pumping lemma (there are other pumping lemmas, but you usually don't talk about them in 601), and a Myhill-Nerode question. There really isn't much reason to not know how to do those and get those questions right. You know they're coming, study for it.
The other thing you can do with the old exams is (surprise) work problems. How do you know if you're right? You don't. If you can, find an elder grad student who took the exams years ago. They likely still have their worked solutions for some old exams somewhere. Get a hold of them and compare some of your answers. Naturally, there's no reason to believe that they worked the problem correctly, but you can at least compare methods.
Most grad students start preparing for the exam in September. That's right, they start 4 months prior to the exam. It can be a lot to study for prelims and also take classes, do research, TA duties, etc. Usually, they take it slow. One week they'll work some architecture problems, the next week they'll do some operating systems problems, etc. Even just finding about 30-60 minutes a night can help. They do more problems when the semester gives them a little break. They do fewer problems when the semesters gets out of hand. They look over the old solutions periodically just to remember what they were doing. When January rolls around, they start working more problems, with maybe one day for theory, the next for algorithms, etc.
Again, this is horribly grad student specific. You may find that you only need a month of prep time. You may think you need less. It's up to you, after all you're the one who's taking the exam.
Good luck!