The first thing you need to keep in mind is that you cannot apply for a permanent visa. Apply for a non-immigrant visa because most universities in the United States do not offer student visa anymore. Students usually get admitted in the F-1 category but for the exchange students, there is another category, J-visa.
If you are looking to apply for admission to an undergraduate program, you must have secondary school qualification at least. You must have English, Mathematics, and Science in addition to an aptitude test usually known as Scholastic Aptitude Test (SAT).
Apart from the basic educational qualification, you need to have some strength in extra-curricular activities. Plus, your performance in admission tests will be taken under serious consideration before selecting you.
For admission to graduates programmes, your basic qualification must be an undergraduate degree. In countries where undergraduate degrees are of two years or three years, the student will be required to take extra courses in Master’s to be eligible for the selection. This is often known as 16th year requirement.
Several admission tests evaluate your admission procedure. Aptitude tests such as GRE, GMAT, TOEFL, IELTS are there to decide your credibility.
For programs like the research Doctorate (PhD) the criteria for admission is usually different in each university. But usually, a student seeking an admission in such program must have a relevant degree in which he is applying for the Doctorate.