I did not do J1.
But if I make a guess, I would say that, like F1, univerisity will send you all necessary documents for you. You then apply get J1 visa at the USA Ambassy in the contry you reside.
Just one advise, better ask for the university to arrange H1. Otherwise you will want to apply for waiver in order to permanently stay (green card) in the US.
Actually you can always ask the university you will go any questions...
Good luck.