It is a rather long process. I had to do it about 5 years ago. First of all you need to get rid of the "2-year homestay requirement" that all J visa holders face.
In my case I wrote to my embassy and they forwarded the letter to my government and then the government released me from the obligation to return home to fullfill the 2-year home stay.
Without that release you CAN NOT change to any other visa type.
My government thru the Embassy sent the satement to the State Department saying that they release me of any previous agreements under the J visa.
Because I don't know if you remember and most of us do not read the fine print, you agree that by accepting the J visa that you will return to your home country after expiration of your J visa and promise to remain there for a period of no less than 2 years.
Once your Embassy forward the paperwork to the State Dept they will notify you, at least in my case they did. The State dept will then send their approval/denial letter to the INS that have jurisdiction over your area. 99.99 % The State dept will give approval as long as it's OK with your government.
In my case I went ahead and contacted the INS and they then told me what form I had to file and the fees. I did that and submitted it to them while they where waiting to hear from the state department, so I did not lose any time. I think it took me about 4-5 months back then. Not sure how long it takes now.