Global Entry membership requires an approved online application followed by an in-person interview at a participating airport. The membership is then tied to your passport - no extra card needed.
Don't worry about filling out the customs declaration during the flight. You'll take care of things on the kiosk later.
After you've landed, look for the Global Entry signs before the long immigration lines.
Scan your passport at an open kiosk, then get your mugshot taken and show them your finger prints.
You'll receive a receipt from the kiosk that can now be given to the ICE officer waiting at the end of the Global Entry area.
You'll be waved right through immigration and on your way to pick up your luggage.