This article is from the FAQ, by with numerous contributions by others.
Any alien who has applied to and been accepted to enroll on a full-time
basis in an academic education program which has been approved by the INS
to accept F-1 applicants is eligible to apply if the student is proficient
in English or engaged in English language courses leading to English
proficiency. The alien must also demonstrate sufficient financial resources
to study without having to work and he or she must also show that there is
no intent to abandon residency in the students home country. Aliens who
are already in the U.S. in a valid status may apply for adjustment of
status to student status. See answer below.