As a J-1 student, you may only be employed and begin working after you have received the appropriate written authorization. Failure to observe this requirement will place you out of status. Also, employers may be cited, fined and/or imprisoned for hiring or maintaining employment for persons who are ineligible.
Authorization typically expires upon completion of your program of studies or the period of lawful stay ends, whichever is sooner or expiration of employment authorizations as noted by USCIS or International Student Services.
(All forms can be found at E-Forms link)