Basically, when you're in high school, you take an aptitude test called the SAT that basically every high school junior or senior takes. You can see some sample questions online, but they test math, reading, and writing skills in a way that highlights critical thinking. You get a score, the highest of which is a 2400. 2400s are few and far between, very rare, and even that isn't enough to get you into an ivy league school.

I toured Stanford once. They were telling us why we shouldn't be too stressed out about our SAT scores and our guide said, "We could fill up an entire class with 2400s. But we don't."

Other things that factor into whether or not you get accepted: GPA (4.0 isn't high enough to get into an ivy. You have to take AP classes, classes that are more challenging, cover more material, and count as a 5 on your transcript), ACT (an equivalent to the SAT. The questions are a little different, and the score is out of 36. This can be taken in addition to or instead of the SAT), and, most importantly,* extracurricular activities.*

If you're an ambitious American student, you better start crafting your story when you're twelve. As soon as we hit middle school, if our parents are aware of how competitive the college system is, they make sure you're involved in community service, or some sort of performing arts (or both. Mostly both). You should play a sport - something rare, like rowing or fencing. If you play an instrument, be a genius at a common one (piano, violin) or amazing at an uncommon one (French horn, bassoon). You absolutely must win contests. Also, start clubs at your school. More than one if possible. Show yourself to be a leader - there are scholarships for that. If you want to do anything in the sciences you should be on your second internship by the time you're starting senior year.

Then in senior year, you start applying. On the common app, you list out every class you took and your grade in that class, your scores on AP tests, on SAT subject tests (different than the regular SAT).

You write your Common App essay. Most colleges accept the Common App as their applicaiton, with additional writing supplements.

If you see someone complaining about the college application process, they're complaining about the writing supplements. In addition to the Common App essay, each college usually requires school-specific essays - anyway from 150 words to 1000 words (and some 1 words...I'm looking at you, Princeton.) These essays ask about your activities, why you want to go to said school, things like that.

You send out all the applications, virtually all colleges ask you send by the internet.

Then you wait. In this time, colleges perform an ancient warlike ritual in which they choose applications seemingly at random and ruin/make lives just willy nilly. I'm not saying this because I'm bitter, I'm saying this because I have seen the most incredible students and wonderful people with GPAs of 4.8 and community service and internships shut out of the ivy league schools.

*TL; DR: * Colleges look at your SAT score to get a sense of how smart you are/how much money your parents had to put you in prep classes.