Every American university is different. There is no centralized admissions system in the US, and different universities have different criteria and standards for admitting students. For graduate study, typically each department handles its own admissions and has its own procedures. So it is impossible to generalize about admission to US universities. You should always check directly with the university and the department to know exactly what they want. University websites provide all the information you need about getting in.

That being said, there are more or less standard guidelines that most universities follow for how to apply and what they look for.

What kinds of documents do you need to prepare to get into a US university? For bachelors or undergraduate study, you will usually need to send:

an application form, which can be submitted electronically or printed from the website and sent by email. Application forms usually ask for biographical information, your academic record and work experience.
An essay, so they can get to know you better. There may be a set question or it may be a general personal statement. Typically they want to know your personality and anything they can't get off of your application. Look to answer questions like "Why do you want to study in the US?", "What do you plan to do with your life?", "What are your biggest achievements?"

The essay is different for every school, and sometimes the topic may seem a little silly, like: "What event in your life was most significant?" or "Who has influenced you the most in your life?" but they want to get to know your character, as well as your academic standing.

Official transcripts--records of your grades--from every secondary school or university you have attended, officially translated into English. Official means stamped by the school or at least verified by a notary.
Letters of recommendation from professors or teachers who know you well. It's better to get a letter from a teacher who had you in class than the director of the school, who never saw you more than once or twice. Letters from high government officials won't do you any good if they don't know you, so resist asking your father to ask his powerful colleagues to write a letter for you.
Most universities require the TOEFL or the IELTS) for international students who have never studied in English before. They will need an official certificate from the organization that administers the test (ETS for the TOEFL).
Sometimes they may require the SAT, another standardized test somewhat like the TOEFL which tests math, language skills, and writing.
Finally, they may ask for a time line or resume, to see what you have been doing since you left secondary school. And you should include seemingly silly things like, reading novels, learning the guitar, playing football with my friends. They want to see if you are a motivated person, or if you just watch TV and sleep in your spare time.
For masters students, you will typically need to send:

The application form from the university
A personal statement explaining what you plan to study, your career goals, what background you have in this area and why you plan to study at this university. Remember to show your personality and also to specifically reference this university. Reminding the school that it has a high ranking or a good reputation is probably not necessary. Look for specific professors, research institutes or options the program offers you. Harvard already knows it's one of the best schools!
Official transcripts from every university you have every attended.
Official TOEFL scores. Or IELTS scores.
GRE or GMAT scores. The GRE is a standardized test much like the SAT which tests math, language skills and writing, and most graduate programs require it for candidates. If you are planning to study business (MBA), accounting, finance, or management, you might need to take the GMAT which tests more advanced math and has an analytical reasoning section. If you plan to get an LLM, you probably won't need either the GRE or GMAT, so check the department website.
Letters of recommendation from professors or even an employer who knows you well and can talk about how well you will study in university.

Again, this list varies for every university and different departments have different requirements so always check. What Gets Me In?

The million dollar question is: what does it take to get into an elite American university? Well, again there is no one answer. Of course, good grades and a high TOEFL score help but the application process in the US tends to be holistic, meaning they look at your whole application together instead of accepting or rejecting you based on only one part. In other words, if you have a low TOEFL score but your resume shows you worked for an American company for two years, they can see you have good English skills and may ignore the low TOEFL score. Of course the opposite is true. If you have good grades, but your essay is very unclear, they may choose to reject you.

The process is also sometimes relative, especially for undergraduates. Your chances of getting in will depend on the competition, what kinds of students are applying that year. If every applicant has perfect grades, then perfect grades won't count for much. That's why it's so hard to get into Harvard--the competition is very high! And again, every university and every department has its own standards, its own idea of the perfect student.

Harvard says on its website that there is no set model of the Harvard student. Some students get in because they are very very good at one thing. Some get in because they are good at a lot of different things. Some people get in because they are highly unique. One big difference between most American universities and many foreign universities is that American universities prize not just academic grades, but also activities in music, theater, public service, even helping your sister do a traditional wedding might be fascinating to a US university. So if you play an instrument, if you are a national champion volleyball player, if you both act in the theater and run a small business selling newspapers, that will help you get in as much as good grades will.

For masters students, work experience is often extremely important and your personal statement will be given a lot of weight. So make sure you have a clear plan of why you want to study and what that will help you accomplish. You don't have to have your whole life planed out, but you should have some idea.

Hopefully this article lets you breathe a little easier since you know what you are facing. Now get to work filling out those applications and writing those essays! Don't hesitate to contact me for more information.

Walton Burns is an English language teacher and university placement consultant in Astana, Kazakhstan. Check out his services at http://www.english.zendurl.com and more of his advice for international students and English language learners at http://www.english.zendurl.com/blog/Blog.html