Single Soldier trying to adopt god son.

I am currently deployed in Iraq. My god sons mother and father decided they couldnt have taking care of him and asked if they could sign his right over to me, or adopt him. Do you know how hard and long it would take? And how can I start this as soon as possible? I am supporting him already while I am over here. If he was my child, i would get benifits for him. He has a few medical problems also.