So one thing people always want to know is how to get into the Columbia Science Honors Program. Well, it's not that hard. Basically, if you like math or science and you're halfway decent, you'll probably get in.
application: just fill it out. Can't help you there.
essay: Basically, you use this to show how much you like science and how good you are at it. I didn't want to sound braggy so I only mentioned my important awards like #1 in school, nationwide, blah blah blah, but I also wrote about my research project in nanobiotechnology which won me some awards and also showed my interest in a specific topic. But I hear the essay doesn't really matter too much, so as long as you don't mess it up too bad, you should be fine.
Recommendation: I don't think this matters that much. Instead of getting one from my chem or calculus teacher, I got it from my AP stats teacher instead. None of my teachers like me, so I was screwed whoever I chose. This doesn't matter much either.
Test: This one is probably the most important part of your acceptance. Lucky for you, the test is also ridiculously easy. If you can get at least 100 on AMC-12, the math part should be a joke for you. It's basically simple geometry and trigonometry with a small amount of probability. There's nothing even close to even AIME level math. Science part is mostly common sense, but reviewing circuits won't hurt you. I got all the circuit problems wrong because I couldn't remember freshman physics...
All in all, the CSHP is a really easy program to get into if you want to get in. I think the test is so easy that if you just review basic science concepts and a little geometry, you can't help but get a hundred. Then again, if you're lazy like me, you'll probably walk into the test room without even knowing what's on the test and do perfectly fine.