I am residing in Georgia. My sponsor is willing to give me the necessary papers for my green card though I am the one to shoulder all expenses. Can I get a green card even though I currently have a J1 visa? What steps do I have to go through?

Since you have a J1, you will first need to request a waiver of the foreign residence requirement (more info at http://www.ins.gov/graphics/howdoi/exchvisit.htm). If you are not sure whether you need a waiver(e.g., did not receive funding from either your country's or the US gov't and your job does not appear in the exchange visitor skill list) then you should probably ask for an advisory opinion (you file this with the Department of State).

I applied for a waiver in May 2001 (even though my visas and IAP-66's all state that I'm not subject to the 2 year rule/ 212(e), the dept of state found otherwise). I'm still waiting. I have a friend who applied a week after I did and got hers in little over 2 months... luck of the draw, I guess. Good luck!!