If you are already in the U.S. on a temporary non-immigrant visa and are looking to change from your current status to an F-1 student visa status, you will first choose the institution (US-Universities List) where you want to study and fill out their international application form. The school must be approved by USCIS to issue F-1 Visas to foreign students. If you have any questions you should contact the admissions department of the school.
Once your international student application is accepted you will obtain form I-20 from the school's DSO and will be added to the SEVIS database.
"Even if you have completed or been terminated from a school, that school is still obligated to transfer your SEVIS record to any school you desire. If your current/previous school refuses to transfer your SEVIS record, work with the DSO at your new school to try to resolve the situation. A school cannot refuse to transfer SEVIS records for any financial or business reasons."