The Institute that sponsors your J1 will do all the paperwork for you. If you don't want to wait until INS approval, you can go to either Mexico or Canada to apply for a physical J1 visa stamp. Once you come back with new J1 visa stamp, you will be in J1 status.
Please note, you may need two J1 waiver, which is impossible, if your J2 was not waivered with J1, your spouse.