A change of visa status to F1 is possible from several visa categories (for example F2, H1, H4). It may be possible to change nonimmigrant status in the U.S. As each situation is different, you must consult with ISSS for details.
The USCIS reviews applications for change of status based on the applicant's ability to document and justify a change of intent upon arrival to the U.S. Applications for change of status shortly after arrival arouse suspicion that the individual purposely misrepresented his/her intentions to obtain a U.S. visa and enter the country.
For more information on changing status in the U.S., see http://www.uscis.gov/i-539.
To request an I-20 for change of status from ISSS click here.