This article is from the FAQ, by with numerous contributions by others.
Yes, if you are currently a genuine nonimmigrant student, you may have been
pursuing a full course of study at the school you were last authorized to
attend during the term immediately preceding the transfer, you intend to be
a full-time student at the new school and you are financially able to attend
the new school.
When you seek a transfer, you must notify the present school of the transfer
and obtain the I-20 AB from the new school. You must complete the Student
Certification portion of the I-20AB and deliver it to the foreign student
officer at the new school within 15 days of beginning attendance at the new
school. The foreign student officer will endorse the transfer on your I-20
copy and return it to you. The foreign student officer then sends the
original I-20 to the INS and a copy to the old school.