It makes me feel so young and hip to get asked advice about taking exams. I've been out of the game for a while, and am not sure I was ever in a position to give much advice. I know what definitely doesn't work.
One of the professors I learned the most from at law school is a guy named Mel Zarr. He made me think in a new and useful way about the law. In many ways, he taught me to think for myself. I took four classes from him, and all of them had twenty-four hour take home exams. I don't think I had any other take homes. The first one was a debacle, described in the post linked above. The other three I did well on, although one of them I postponed working on all day, and finally woke up at 4:30 in the morning, went to the office of the venture capital firm I was working at at the time, and sat in their kitchen in the dull fluorescent lights, writing my answer in a blind, rushed panic before turning it in at 8:30. I got a really good grade on that one. It doesn't make any sense to me.
Here's what you need to face with a take-home exam: preparation and procrastination. You need to be adequately prepared, but if you've prepared too well you may be lackadaisical about the exam itself. And no matter how well you've prepared, if there's too much time allocated for the exam you need to face your own tendency to procrastinate. Mine was rather extreme as a law student. I needed to get quite close to panic before I could overcome the desire to fritter my time away on pointless things. It's not really an ideal way to work.
Make sure your printer works -- enough ink, paper, cables, nothing funny. It's no fun to battle with printers when you're in a blind panic and running late. Make sure you have snacks and caffeine. Otherwise don't worry too much about it. Get your notes in order, and think about the themes of the course -- what's it all about, anyway? But don't overstudy. You'll do a better job figuring out what you need to think about when you have the question in front of you.
With a take home exam you have a little bit of time to let the question open up for you. I used to read the question and think, good heavens, I have no idea what this is even asking for. And then I'd wait a little while and see something in there. And I'd wait a little longer and understand more. And then I'd start writing and I'd start to feel like maybe I knew what the question was about, and maybe had a few things to say about it. And then I'd go back and reread notes and materials and the question again and I'd see a bunch of stuff I'd missed the first couple of times around and by then I'd start to have an idea of what the professor really wanted and what I wanted to say about it, and it would get to be kind of fun. That gradual process wasn't something the three-hour in-class exam really permitted. So it may sound perverse, but enjoy the take home, if you can.