You go through the normal lines, just ask which one you should go through and if possible have the envelope out and ready to show them and tell them you are entering for the first time on a GC. At Boston, the guy at the desk did the first check. We all went through as a family, he asked some very basic questions and then called over a colleague to escort us to a room downstairs by baggage claim. We were told to wait until an another officer could process the paperwork. There were only 2 other immigrants in the room at the time and I don't think they were there for the same reason as us. So we got seen pretty quickly. I was just hanging back with my daughter while my husband went up to the desk and got asked a few more questions. He was told a few things about the GC process and when to expect certain docs to arrive and we were done. All in all....maybe 30 minutes. But Boston doesn't have a huge volume of international flights.
Good luck.